Abstract
In the first part of the paper there is given a survey of the contemporary state of the theory of the sufficient univalence and p-valence conditions for analytic and meromorphic functions of a complex variable. The second part is devoted to a survey of the results on the conditions for the univalent solvability of applied inverse boundary value problems.
Similar content being viewed by others
Literature cited
R. G. Avkhadiev, “A special case of the Schwarz problem and some of its applications,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 15, 3–15 (1978).
R. G. Avkhadiev, “On an exterior inverse boundary value problem in Cartesian coordinates for a doubly connected domain,” Mariisk. Univ., Poshkar-Ola (1982). (Manuscript deposited at VINITI, Nov. 23, 1982, No. 5797-82 Dep.)
R. G. Avkhadiev and L. N. Zhurbenko, “A certain generalization of the inverse boundary value problem in x and the stability of its solution,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 14, 5–19 (1977).
R. G. Avkhadiev and L. N. Zhurbenko, “On inverse boundary value problems in polar coordinates with singular points on the boundaries,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 16, 3–14 (1979).
F. G. Avkhadiev, “Radii of convexity and almost convexity of certain integral representations,” Mat. Zametki,7, No. 5, 581–592 (1970).
F. G. Avkhadiev, “On sufficient conditions for the univalence of the solutions of inverse boundary value problems,” Dokl. Akad. Nauk SSSR,190, No. 3, 495–498 (1970).
F. G. Avkhadiev, “On univalence conditions of analytic functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 745–748 (1970).
F. G. Avkhadiev, “Some sufficient conditions for the univalence of the solutions to applied inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 8, 3–11 (1971).
F. G. Avkhadiev, “Some sufficient conditions for the univalence of analytic functions,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 9, 3–11 (1972).
F. G. Avkhadiev, “On weak and strong univalence problems in inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 10, 3–10 (1973).
F. G. Avkhadiev, “Sufficient conditions for univalence in nonconvex domains,” Sib. Mat. Zh.,15, No. 5, 963–971 (1974).
F. G. Avkhadiev, “On certain univalent mappings of the half plane,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 11, 3–8 (1974).
F. G. Avkhadiev, “Sufficient conditions for the univalence of quasiconformal mappings,” Mat. Zametki,18, No. 6, 793–802 (1975).
F. G. Avkhadiev, “Singular cases of the principle of correspondence of boundaries,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 13, 13–23 (1976).
F. G. Avkhadiev, “On sufficient conditions for pseudoanalytic continuability,” in: Theory of Mappings, Its Generalizations and Applications [in Russian], Naukova Dumka, Kiev (1982), pp. 3–9.
F. G. Avkhadiev, “On the univalence of mappings with given boundary properties,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 19, 3–14 (1983).
F. G. Avkhadiev, “Certain geometric inequalities and sufficient conditions forp-valence,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 3–12 (1983).
F. G. Avkhadiev, “On the method of locally homeomorphic extension in the theory of sufficient univalence conditions,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 20, 3–10 (1983).
F. G. Avkhadiev, “An inverse boundary value problem for a function with singularities,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 3–19 (1984).
F. G. Avkhadiev, “On an inverse boundary value problem for a function with a pole and a logarithmic singularity,” in: Proceedings of a Commemorative Seminar on Boundary Value Problems, Dedicated to F. D. Gakhov, Academician of the Academy of Sciences of the Belorussian SSR on the 75th Anniversary of his Birth (Minsk, 1981), Minsk (1985), pp. 139–142.
F. G. Avkhadiev, “Classes of at mostp-valent mappings in an annulus,” in: Problems in the Theory of Special Classes of Functions [in Russian], Stavropol (1985), pp. 3–16.
F. G. Avkhadiev and L. A. Aksent'ev, “Sufficient conditions for the univalence of analytic functions,” Dokl. Akad. Nauk SSSR,198, No. 4, 743–746 (1971).
F. G. Avkhadiev and L. A. Aksent'ev, “A subordination principle in sufficient conditions for univalence,” Dokl. Akad. Nauk SSSR,211, No. 1, 19–22 (1973).
F. G. Avkhadiev and L. A. Aksent'ev, “Functions of the Bazilevich class in a circle and in an annulus,” Dokl. Akad. Nauk SSSR,214, No. 2, 241–244 (1974).
F. G. Avkhadiev and L. A. Aksent'ev, “Fundamental results on sufficient conditions for the univalence of analytic functions,” Usp. Mat. Nauk,30, No. 4, 3–60 (1975).
F. G. Avkhadiev and L. A. Aksent'ev, “Achievements and problems in sufficient conditions for the finite-valence of analytic functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 3–16 (1986).
F. G. Avkhadiev, L. A. Aksent'ev, and A. M. Elizarov, “Univalence tests for the solutions of applied inverse boundary value problems. I,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 23, 6–24 (1987).
F. G. Avkhadiev and S. R. Nasyrov, “Necessary conditions for the existence of a Riemann surface with a prescribed boundary,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 22, 6–15 (1985).
F. G. Avkhadiev and S. R. Nasyrov, “The construction of a Riemann surface from its boundary,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 3–11 (1986).
F. G. Avkhadiev and N. B. Salimov, “The univalent solvability of the inverse boundary value problem of blast theory,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 13, 24–29 (1976).
F. G. Avkhadiev and P. L. Shabalin, On mappings on multiply connected domains that do not belong to V. I. Smirnov's class. Kazan. Univ., NII Mat. Mekh., Kazan (1976). (Manuscript deposited at VINITI, July 6, 1976, No. 2550-76 Dep.)
L. A. Aksent'ev, “Sufficient conditions for the univalence of the solutions of three inverse boundary value problems,” Uch. Zap. Kazan. Univ., 117, Book 2, 32–35 (1957).
L. A. Aksent'ev, “Sufficient conditions for the univalence of the solution of an inverse boundary value problem of the theory of filtration,” Usp. Mat. Nauk,14, No. 4, 133–140 (1959).
L. A. Aksent'ev, “Conditions for the univalence of solutions of the fundamental inverse boundary value problems,” Usp. Mat. Nauk,15, No. 6, 119–124 (1960).
L. A. Aksent'ev, “The univalent variation of the profile of a dam,” in: Studies in the Modern Problems of the Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1960), pp. 335–340.
L. A. Aksent'ev, “On the univalence of the solution of an inverse problem in hydrodynamics,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 3–7 (1961).
L. A. Aksent'ev, “Geometric aspects in inverse boundary value problems,” Trudy Sem. Obratn. Kraev. Zadacham, Kazan. Univ., No. 1, 14–18 (1964).
L. A. Aksent'ev, “On conditions for solvability and for univalence,” Trudy Sem. Obratn. Kraev. Zadacham, Kazan. Univ., No. 2, 12–20 (1964).
L. A. Aksent'ev, “Sharp estimates for harmonic functions in the circle,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 3–8 (1968).
L. A. Aksent'ev, “Application of the argument principle to the investigation of univalence conditions. I,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 3–15 (1968).
L. A. Aksent'ev, “Application of the argument principle to the investigation of univalence conditions. II,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 3–15 (1969).
L. A. Aksent'ev, “On the univalent solvability of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 10, 11–24 (1973).
L. A. Aksent'ev, “On the univalent solvability of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan, Univ., No. 11, 9–18 (1974).
L. A. Aksent'ev, “Univalent variation of polygonal domains,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 13, 30–39 (1976).
L. A. Aksent'ev, “Symmetric solutions of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 14, 20–27 (1977).
L. A. Aksent'ev, “Sufficient conditions for multivalence of integral representations,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 17, 3–17 (1980).
L. A. Aksent'ev, “The connection of the exterior inverse boundary value problem with the inner radius of the domain,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 3–11 (1984).
L. A. Aksent'ev, Collection of Problems in the Theory of Functions of a Complex Variable and Operational Calculus [in Russian], Kazan. Univ., Kazan (1984).
L. A. Aksent'ev, V. N. Gaiduk, and V. P. Mikka, “Univalence criteria for n-symmetric functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 3–13 (1974).
L. A. Aksent'ev, V. N. Gaiduk, and V. P. Mikka, “On the univalent solvability of the inverse boundary value problem for a regular function in a doubly connected domain,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 12, 3–8 (1975).
L. A. Aksent'ev and N. A. Gubaidullina, “An application of skeletal polygons to the univalent solvability of boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 13, 40–48 (1976).
L. A. Aksent'ev, A. M. Elizarov, and M. I. Kinder, “Continuation of F. D. Gakhov's work in inverse boundary value problems,” Proc. of a Commemorative Seminar on Boundary Value Problems Dedicated to the 75th Birthday of Acad. F. D. Gakhov (Minsk, 1981) [in Russian], Minsk (1985), pp. 30–43.
L. A. Aksent'ev, A. M. Elizarov, and M. I. Kinder, “Inverse boundary value problems for multiply connected domains on Riemann surfaces of genus zero. I,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 19–32 (1984).
L. A. Aksent'ev, A. M. Elizarov, and M. I. Kinder, “Inverse boundary value problems for multiply connected domains on Riemann surfaces of genus zero. II,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 22, 16–29 (1985).
L. A. Aksent'ev, A. M. Elizarov, and M. I. Kinder, “Inverse boundary value problems for multiply connected domains on Riemann surfaces of genus zero. III,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 23, 25–36 (1987).
L. A. Aksent'ev, A. M. Elizarov, and M. I. Kinder, “A proof of the solvability of inverse boundary value problems by the method of vector fields,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 82–84 (1986).
L. A. Aksent'ev and L. N. Zhurbenko, “Questions of well-posedness in inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 16, 15–28 (1979).
L. A. Aksent'ev, N. B. Il'inskii, M. T. Nuzhin, R. B. Salimov, and G. G. Tumashev, “The theory of inverse boundary value problems for analytic functions and its applications,” Itogi Nauki i Tekhniki, Ser. Mat. Analiz,18, 67–124 (1980).
L. A. Aksent'ev, A. V. Hazantsev, and A. V. Kiselev, “On the uniqueness of the solution of an exterior inverse boundary value problem,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 8–18 (1984).
L. A. Aksent'ev, M. I. Kinder, and S. B. Sagitova, “Solvability of the exterior inverse boundary value problem in the case of a multiply connected domain,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 20, 22–34 (1983).
L. A. Aksent'ev and S. N. Kudryashov, “Certain conditions for the univalence of the solution of an inverse boundary value problem for a symmetric profile,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 6, 3–15 (1969).
L. A. Aksent'ev and F. F. Maier, “Application of methods of subordination and symmetrization to sufficient tests of univalence of analytic functions,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 19, 14–28 (1983).
L. A. Aksent'ev and I. R. Nezhmetdinov, “Sufficient conditions for the univalence of certain integral representations,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 18, 3–11 (1982).
L. A. Aksent'ev and Yu. A. Reshetnikov, “On univalent solvability of inverse problems of hydromechanics,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 8, 12–21 (1971).
L. A. Aksent'ev and Yu. A. Reshetnikov, “Investigations on questions of solvability and univalence in velocity hodograph problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 9, 12–22 (1972).
L. A. Aksent'ev and Yu. A. Reshetnikov, “On the monotonicity of the mean values of subharmonic functions in an annulus,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 3–10 (1981).
L. A. Aksent'ev, Yu. E. Khokhlov, and E. A. Shirokova, “On the uniqueness of the solution of the exterior inverse boundary value problem,” Mat. Zametki,24, No. 3, 319–330 (1978).
L. A. Aksent'ev and P. L. Shabalin, “On S. N. Andrianov's problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 14, 28–35 (1977).
L. A. Aksent'ev and P. L. Shabalin, “Conditions for univalence in star-shaped and convex domains,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 20, 35–42 (1983).
L. A. Aksentev and P. L. Shabalin, “Conditions for univalence with a quasiconformal extension and their application,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 6–14 (1983).
I. A. Aleksandrov, “On a case of integration of the Lowner equation,” Sib. Mat. Zh.,22, No. 2, 207–209 (1981).
I. A. Aleksandrov, Parametric Continuations in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1976).
Yu. E. Alenitsyn and S. Ya. Khavinson, “On the radius of p-valence for bounded analytic functions in multiply connected domains,” Mat. Sb.,52 (94), 653–657 (1960).
L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand Princeton (1966).
S. N. Andrianov, “On the existence and the number of solutions of the inverse boundary value problem in the theory of analytic functions,” Uch. Zap. Kazan. Univ.,113, No. 10, 21–30 (1953).
I. E. Bazilevich, “Generalization of an integral formula for a subclass of univalent functions,” Mat. Sb.,64 (108), No. 4, 628–630 (1964).
I. E. Bazilevich, “A criterion for the univalence of regular functions with a positive Hayman constant,” Mat. Sb.,116 (158), No. 3, 291–298 (1981).
B. D. Bayachorova, “Algorithm for conclusive coefficient bounds in the univalence conditions according to Nehari's theorem,” in: Algoritmy, No. 47, 87–91 (1982).
P. P. Belinskii, General Properties of Quasiconformal Mappings [in Russian], Nauka, Novosibirsk (1974).
A. Ya. Bokareva and G. I. Maikapar, “The approximate construction of a thin profile from a given pressure,” Tr. TsAGI, No. 663, 31–38 (1948).
A. V. Bondar', “On conditions for the homeomorphism of holomorphic mappings with singularities,” in: Theory of Functions and Topology, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1983), pp. 7–12.
A. A. Brodskii and Yu. E. Khokhlov, “On deformations and attainability from the outside of domains in Cn,” Donetsk. Univ. (1983). (Manuscript deposited at Ukr.NIINTI, No. 321 Uk D84.)
O. A. Busovskaya, “Geometric characterization of subclasses of univalent functions,” Ukr. Mat. Zh.,37, No. 5, 558–562 (1985).
O. A. Busovskaya and V. V. Goryainov, “On a homeomorphic extension of spiral functions,” Ukr. Mat. Zh.,33, No. 5, 656–660 (1981).
N. N. Vidyakina, “The fundamental inverse boundary value problem for domains that are biholomorphically equivalent to the bidisc,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 17–26 (1974).
V. N. Gaiduk, “The application of typically real functions to inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 6, 26–30 (1969).
V. N. Gaiduk, “Some univalence conditions for the solutions of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 7, 98–102 (1970).
V. N. Gaiduk, “Some univalence conditions for the solution of an inverse boundary value problem forn-symmetric functions,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 8, 55–58 (1971).
V. N. Gaiduk and E. L. Melkonyan, “Some univalence conditions ofn-symmetric functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 45–50 (1974).
N. A. Galeeva, “On the inverse problem of the filtration for a permeable contour,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 8, 59–65 (1971).
V. N. Gaiduk and Yu. A. Reshetnikov, “On the univalence of the solution of an inverse problem in the theory of filtration,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 9, 49–56 (1972).
F. D. Gakhov, “On inverse boundary value problems,” Dokl. Akad. Nauk SSSR,86, No. 4, 649–652 (1952).
F. D. Gakhov, “On inverse boundary value problems,” Uch Zap. Kazan. Univ.,113, No. 10, 9–20 (1953).
F. D. Gakhov, “Inverse boundary value problems,” in: History of National Mathematics, Vol. 4, Book 1, Naukova Dumka, Kiev (1970), pp. 253–264.
F. D. Gakhov, E. I. Zverovich, and S. G. Samko, “Increment of the argument, logarithmic residue and a generalized principle of the argument,” Dokl. Akad. Nauk SSSR,213, No. 6, 1233–1236 (1973).
F. D. Gakhov and Yu. M. Krikunov, “Topological methods in the theory of functions of a complex variable and their application to inverse boundary value problems,” Izv. Akad. Nauk SSSR, Ser. Mat.,20, No. 2, 207–240 (1956).
V. D. Golovan', “On the question of smoothness of the boundary of domains under univalent mappings, ” Sib. Mat. Zh.,24, No. 6, 202–203 (1983).
G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Am. Math. Soc., Providence (1969).
N. A. Gubaidullina, “Univalence conditions for the solutions of the mixed boundary value problem, and their application to the problem of filtration under pressure,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 12, 32–38 (1975).
N. A. Gubaidullina, “On the univalence of a certain integral representation,” in: Theory of Mappings, Its Generalizations and Applications [in Russian], Naukova Dumka, Kiev (1982), pp. 68–74.
E. Goursat, Cours d'Analyse Mathematique, Tome II, Gauthier-villars, Paris (1933).
V. Ya. Gutlyanskii, “On the fibering of the class of univalent analytic functions,” Dokl. Akad. Nauk SSSR,196, No. 3, 498–501 (1971).
G. V. Danilova, “The construction of the underground profile of hydroconstructions under an inclined water confining layer,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 3, 25–27 (1966).
G. V. Danilova and N. B. Salimov, “On an inverse boundary value problem in the theory of filtration,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 7, 116–121 (1970).
E. P. Dolzhenko, “On the ‘obliteration’ of the singularities of analytic functions,” Usp. Mat. Nauk,18, No. 4, 135–142 (1963).
A. M. Elizarov, “On the stability of the solutions of inverse mixed boundary value problems on the example of problems in the theory of filtrations,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 54–63 (1977).
A. M. Elizarov, “Proof of the solvability of certain mixed inverse boundary value problems for a regular function,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 94–98 (1979).
A. M. Elizarov, “On the solvability of a mixed inverse boundary value problem for a doubly connected domain,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 73–76 (1980).
A. M. Elizarov, “The investigation of questions on the well-posedness of exterior mixed inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 17, 44–55 (1980).
A. M. Elizarov, “On a mixed inverse boundary value problem on the flow around an arbitrary profile,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 17, 56–62 (1980).
A. M. Elizarov, “On a certain class of mixed inverse boundary value problems,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 28–34 (1981).
A. M. Elizarov, “On a certain interior mixed inverse boundary value problem,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 77–80 (1981).
A. M. Elizarov, “On a mixed inverse boundary value problem with respect to the parameter r- ¦z¦,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 26–32 (1981).
A. M. Elizarov, “Jet flow around a nonsmooth curvilinear obstacle,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 11–20 (1983).
A. M. Elizarov, “On mixed inverse boundary value problems in doubly connected domains,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 18, 53–61 (1982).
A. M. Elizarov, “On the Leray constraint in application to mixed inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 20, 74–92 (1983).
A. M. Elizarov, “On the integral equations of mixed inverse boundary value problems,” in: Constructive Theory of Functions and Functional Analysis, No. 3 [in Russian], Kazan. Gos. Univ., Kazan (1981), pp. 16–25.
A. M. Elizarov, “On the quasisolutions of an exterior inverse boundary value problem,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 42–50 (1984).
A. M. Elizarov and N. B. Ilinskii, “The determination of the flood-bed contour from the velocity profile in the presence of a confining layer,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 19, 59–72 (1983).
A. M. Elizarov and N. B. Il'inskii, “The method of quasisolutions in an inverse boundary value problem of hydroaerodynamics,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 50–59 (1984).
A. M. Elizarov and N. B. Il'inskii, “On the method of quasisolutions in the inverse boundary value problem of hydroaerodynamics,” in: Complex Methods in Mathematical Physics. Abstracts of Reports. All-Union School of Young Scientists, Donetsk (1984), p. 141.
A. M. Elizarov, N. B. Il'inskii, and A. V. Potashev, “Quasisolutions of the inverse boundary value problem of hydroaerodynamics,” Dokl. Akad. Nauk SSSR,284, No. 2, 319–322 (1985).
A. M. Elizarov, N. B. Il'inskii, and A. V. Potashev, “On prescribing the distribution of velocities at the construction of an isolated wing profile by the method of quasisolutions,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 22, 69–78 (1985).
A. M. Elizarov, N. B. Il'inskii, and A. V. Potashev, “The construction of wing profiles on the basis of the theory of inverse boundary value problem by the method of quasisolutions,” Izv. Vyssh. Uchebn. Zaved., Aviatsion. Tekh., No. 3, 18–22 (1986).
A. M. Elizarov, N. B. Il'inskii, and A. V. Potashev, “On a new approach in the design of wing profiles,” in: Modern Problems in Mechanics and in Machine Construction Technology. Abstract of Reports. All-Union Conference. April 22–24, 1986, Moscow (1986).
A. M. Elizarov, N. B. Il'inskii, and A. V. Potashev, “The construction of wing profiles by the method of the quasisolutions of inverse boundary value problem,” in: Sixth All-Union Congress of Theoretical and Applied Mechanics, 1986. Synopses of Reports, Tashkent (1986), p. 265.
A. M. Elizarov, N. B. Il'inskii, and A. V. Potashev, “The inverse boundary value problem for an isolated wing profile with suction,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 23, 61–69 (1987).
A. M. Elizarov and V. V. Seleznev, “On the solvability of certain mixed inverse boundary value problems on a flow around a profile,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 3–10 (1981).
I. V. Zhuravlev, “Some sufficient conditions of quasiconformal continuability of analytic functions,” Dokl. Akad. Nauk SSSR,243, No. 6, 1377–1380 (1978).
I. V. Zhuravlev, “Univalent functions and Teichmuller spaces,” Dokl. Akad. Nauk SSSR,250, No. 5, 1047–1050 (1980).
I. V. Zhuravlev, “Conditions for quasiconformal continuability of analytic functions,” in: Theory of Mappings, Its Generalizations and Applications [in Russian], Naukova Dumka, Kiev (1982), pp. 84–91.
I. V. Zhuravlev, “Sufficient conditions for the univalence and the quasiconformal extendability of holomorphic functions,” in: Complex Methods in Mathematical Physics. Abstracts of Reports. All-Union School of Young Scientists, Donetsk (1984), p. 203.
M. N. Zhuravlev, “An inverse boundary value problem of magnetostatics,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 8, 80–85 (1971).
L. N. Kuznetsova, “On the uniqueness and stability of the solutions of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 11, 131–137 (1974).
L. N. Kuznetsova, “On the stability of the solutions of inverse boundary value problems in the spaceC k,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 12, 141–152 (1975).
L. N. Kuznetsova, “On the stability of the solution of the exterior inverse boundary value problem,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 13, 167–174 (1976).
L. N. Kuznetsova, “Stability of the solutions of interior inverse boundary value problems,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 43–53 (1976).
L. N. Zhurbenko, “On the stability of the solutions of inverse boundary value problems for multiply connected domains in the case of the parameter x,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 31–41 (1979).
L. N. Zhurbenko, “On the stability of the solution of an inverse boundary problem with a parameters in the case of a multiply connected domain,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 17, 74–84 (1980).
L. N. Zhurbenko, “Inverse boundary value problems with singularities on the boundaries for multiply connected domains,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 18, 68–79 (1982).
L. N. Zhurbenko and S. B. Sagitova, “On inverse boundary value problems with mixed parameters for doubly connected domains,” Kazan. Univ. No. 5779-82, Kazan (1982).
T. A. Zapuskalova and B. A. Kats, “A Riemann boundary value problem on a spiral-shaped contour,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 15, 53–61 (1978).
E. I. Zverovich, “Boundary value problems in the theory of analytic functions in Hölder classes on Riemann surfaces,” Usp. Mat. Nauk,26, No. 1, 113–179 (1971).
E. I. Zverovich, “A method of locally conformal gluing,” Dokl. Akad. Nauk SSSR,205, No. 4, 767–770 (1972).
P. M. Zinov'ev, “Univalence conditions for analytic functions in a half plane and their application to inverse boundary value problems,” Kazan. Univ., Kazan (1983). (Manuscript deposited at VINITI, Apr. 5, 1983, No. 1704-83 Dep.)
P. M. Zinov'ev, “A sufficient univalence condition for the solution of the problem of the construction of a doubly periodic hydrodynamic lattice,” Kazan. Univ., Kazan (1983). (Manuscript deposited at VINITI, Aug. 15, 1983, No. 4469-83 Dep.)
P. M. Zinov'ev, “Conditions for the univalence of nonanalytic functions in the half plane,” in: Theory of Functions and Approximations. Proc. Saratov winter School, 1982, Part 2, Saratov (1983), pp. 56–59.
P. M. Zinov'ev, “Sufficient conditions for univalence of the solution of an inverse boundary value problem in the case of an infinite unknown contour,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 77–86 (1984).
P. M. Zinov'ev and F. F. Maier, “Conditions for univalence of symmetric functions in a strip and half-plane and their application,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 61–64 (1984).
V. A. Zmorovich and L. A. Gudz', “On certain classes of univalent functions in the circle ¦z¦<1 and in the domain ¦z¦>1,” in: Mathematical Analysis and Probability Theory [in Russian], Naukova Dumka, Kiev (1978), pp. 59–63.
V. A. Zorich, “Quasiconformal mappings in the geometric theory of functions,” in: Modern Problems in the Theory of Functions, Baku (1980), pp. 18–30.
Kh. D. Zung, “On the stability of an inverse boundary value problem in the theory of analytic functions,” Izv. Akad. Nauk BSSR, Ser. Fiz. Mat. Nauk, No. 4, 2226 (1967).
Kh. D. Zung, “The stability of an inverse boundary value problem in the case of the multivalence of the solution and some generalizations,” Izv. Akad. Nauk BSSR, Ser. Fiz. Mat. Nauk, No. 4, 26–30 (1968).
Kh. D. Zung, “On the stability of an inverse boundary value problem for a multiply connected domain,” Izv. Akad. Nauk BSSR, Ser. Fiz. Mat. Nauk, No. 2, 33–37 (1969).
V. K. Ivanov, “On ill-posed problems,” Mat. Sb.,61, No. 2, 211–223 (1963).
V. K. Ivanov, V. V. Vasin, and V. P. Tanana, Theory of Linear Ill-Posed Problems and Its Applications [in Russian], Nauka, Moscow (1978).
N. B. Il'inskii and A. R. Kasimov, “The optimization of the form of a ground channel by the method of inverse boundary value problems,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 76–80 (1984).
N. B. Ilinskii and S. R. Nasyrov, “On the problem of constructing a flood-bed from the counterpressure profile,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 16–23 (1982).
N. B. Il'inskii and S. R. Nasyrov, “The problem of the determination of the underground contour from the counterpressure profile in the presence of a rectilinear confining layer,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 34–42 (1984).
N. B. Il'inskii and A. V. Potashev, The Boundary Value Problems of Blast Theory [in Russian], Kazan. Univ., Kazan (1986).
N. B. Il'inskii and R. B. Salimov, “The inverse problem of blast theory,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 51–57 (1974).
A. R. Kasimov, “Filtration optimization of the shape of a ground channel taking into account capilarity,” in: Contemporary Problems and Mathematical Methods in the Theory of Filtration [in Russian], Moscow (1984), pp. 144–145.
A. R. Kasimov, “The filtration calculation of a drainage by the method of the inverse boundary value problem,” Kazan. Univ., Kazan (1985). (Manuscript deposited at VINITI, Aug. 27, 1985, No. 2129-85 Dep.)
A. R. Kasimov, “The solution of isoperimetric problems of a plane stegdy-state filtration by the inverse method,” in: Sixth All-Union Congress on Theoretical and Applied Mechanics (1986). Abstract of Communications [in Russian], Tashkent (1986), p. 335.
S. A. Kas'yanyuk, “On the method of structural formulas and the principle of correspondence of boundaries under conformal mappings,” Dokl. Akad. Nauk Ukr. SSR, No. 1, 14–17 (1959).
S. Kasymov, “On the univalence of analytic functions,” in: Mathematical Analysis and Its Applications, No. 7 [in Russian], Rostovsk. Univ. (1975), pp. 96–102.
S. Kasymov, “Tests for the univalence of analytic functions, and their application,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 38–42 (1977).
S. Kasymov, “Some sufficient conditions for the univalence of functions and their applications,” in: Mathematical Analysis and Its Applications [in Russian], Rostovsk. Univ. (1981), pp. 65–71.
B. A. Kats, “A boundary value problem with nonhomeomorphic shift,” Dokl. Akad. Nauk SSSR,219, No. 4, 781–784 (1974).
B. A. Kats, “The Riemann problem on a closed Jordan curve,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 68–80 (1983).
B. A. Kats, “A Riemann boundary value problem on an open Jordan curve,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 56–60 (1986).
B. A. Kats and S. R. Mironova, “On the Riemann boundary value problem on a countable set of curves with coefficients admitting power singularities,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 71–74 (1986).
M. I. Kinder, “On the number' of solutions of F. D. Gakhov's equation in the case of a multiply connected domain,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 69–72 (1984).
M. I. Kinder, “The investigations of F. D. Gakhov's equation in the case of a multiply connected domain,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 22, 104 116 (1985).
V. V. Klokov, Kazan. Univ., Kazan (1984).
A. N. Kolmogorov and V. M. Tikhomirov, “ε-entropy andε-capacity of sets in functional spaces,” Usp. Mat. Nauk,14, No. 2, 3–86 (1959).
V. K. Kochetkov, “On certain solutions of a differential equations of univalent functions,” in: Differential and Integral Equations and Their Applications [in Russian], Kalmytsk. Gos. Univ., Elista (1983), pp. 73–78.
I. S. Krasnovodina and V. S. Rogozhin, “A sufficient condition for the univalence of the solution of an inverse boundary value problem,” Usp. Mat. Nauk,8, No. 1, 151–153 (1953).
S. L. Krushkal', “Differential operators and univalent functions,” Dokl. Akad. Nauk SSSR,280, No. 3, 541–544 (1985).
M. R. Kuvaev, “A generalization of the Loewner type equation for automorphic functions,” Trudy Tomsk. Univ. Sekts. Mat. Mekh. Astron.,144, 27–30 (1959).
S. N. Kudryashov, “On the uniqueness of the solutions of exterior inverse boundary value problems,” in: Materials of the Fourth Scientific Conference of the Aspirants of Rostov University [in Russian], Rostov-on-the-Don (1962), pp. 56–59.
S. N. Kudryashov, “Some sufficient conditions for the univalence of the solution of an inverse problem of the theory of filtration,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 88–99 (1966).
S. N. Kudryashov, “On the number of solutions of exterior inverse boundary value problems,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 30–32 (1969).
S. N. Kudryashov, “On certain tests for the univalence of analytic functions, ”Mat. Zametki,13, No. 3, 359–366 (1973).
S. N. Kudryashov and F. G. Avkhadiev, “On the number of solutions of an exterior inverse boundary value problem,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 8, 136–143 (1971).
S. N. Kudryashov and S. Kasymov, “On univalence conditions for certain classes of analytic functions and their applications,” No. 2458-76. Kazan. Univ., Kazan (1976).
S. N. Kudryashov and A. F. Patalakh, “The Schwarz invariant and conditions for univalence of meromorphic functions,” in: Mathematical Analysis and Its Applications [in Russian], Rostov. Gos. Univ., Rostov-on-Don (1983), pp. 41–49.
S. N. Kudryashov and A. P. Tikhonov, “On a test for the univalence of an analytic function,” in: Mathematical Analysis and Its Applications [in Russian], Rostov. Univ., Rostov-on-the-Don (1974), pp. 90–93.
G. V. Kuz'mina, “Geometric theory of functions: methods and results,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 17–32 (1986).
M. A. Lavrent'ev, “Sur une classe de representations continues,” Mat. Sb.,42, No. 4, 407–424 (1935).
M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1973).
M. M. Lavrent'ev (M. M. Lavrentiev), Some Improperly Posed Problems of Mathematical Physics, Springer, New York (1967).
M. M. Lavrent'ev, Conditionally Well-Posed Problems for Differential Equations [in Russian], Novosibirsk State Univ. (1973).
I. A. Lebedev, “On integrating factors of the Loewner-Kufarev equation,” Vestn. Leningr. Univ., Mat. Mekh. Astron., No. 13, Vyp. 3, 107–109 (1981).
I. A. Lebedev, “On structural formulas of Bazilevich type,” Vestn. Leningr. Univ., Mat. Mekh. Astron. No. 19, vyp. 4, 114–116 (1981).
I. A. Lebedev, “On structural formulas for univalent functions,” J. Sov. Math.,26, No. 6 (1984).
N. A. Lebedev, “On the univalence of a certain class of functions,” Vestn. Leningr. Univ., Mat. Mekh. Astron. No. 1, 113–115 (1981).
G. S. Litvinchuk, Boundary Value Problems and Singular Integral Equations with a Shift [in Russian], Nauka, Moscow (1977).
F. F. Maier, “The extension of the class of star-shaped functions with the aid of Becker's condition,” Kazan. Univ., Kazan (1982). (Manuscript deposited at VINITI, Nov. 23, 1982, No. 5780-82 Dep.)
F. F. Maier, “On sufficient tests for univalence of n-symmetric solutions of inverse boundary value problems,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 80–82 (1983).
F. F. Maier, “Estimates for functions that are regular in the circle and their applications,” in: Theory of Functions and Approximation, Proc. Saratov winter School, 1982, Part 2, Saratov (1983), pp. 85–88.
F. F. Maier, “Majorization of analytic functions in certain classes and its application,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 57–66 (1986).
V. P. Mikka, “Sufficient conditions for the univalence of the solutions of inverse boundary value problems with angular points,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 10, 95–106 (1973).
V. P. Mikka, “Two sufficient conditions for the univalence of analytic functions,” Mat. Zametki,19, No. 3, 331–346 (1976).
V. P. Mikka, “On the univalence of analytic functions with bounded curvature,” Trudy Sem. Hraev. Zadacham, Kazan. Univ., No. 19, 115–122 (1983).
Yu. A. Mitropol'skii, P. M. Tamrazov, and L. A. Gudz', “V. A. Zmorovich's investigations in the field of the geometric theory of functions,” Ukr. Mat. Zh.,31, No. 6, 756–760 (1979).
I. P. Mityuk, Symmetrization Methods and Their Application to the Geometric Theory of Functions. Introduction to Symmetrization Methods [in Russian], Kubansk. Univ. (1980).
I. P. Mityuk, The Application of Symmetrization Methods to Geometric Function Theory [in Russian], Kubansk. Univ. (1985).
I. P. Mityuk, V. G. Sheretov, and E. A. Shcherbakov, Plane Quasiconformal Mappings [in Russian], Kubansk. Univ. (1979).
V. N. Monakhov, Boundary Value Problems with Free Boundaries for Elliptic Systems of Equations [in Russian], Nauka, Novosibirsk (1977).
M. Morse, Topological Methods in the Theory of Functions of a Complex Variable, Princeton Univ. Press, Princeton (1947).
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).
S. R. Nasyrov, “On the method of polygonal approximation in mixed inverse boundary value problems with respect to the parameter x,” Kazan. Univ., NII Mat. i Mekh., Kazan (1982). (Manuscript deposited at VINITI, May 17, 1982).
S. R. Nasyrov, “On quasiconformal extension for a class of univalent functions,” in: Theory of Mappings, Its Generalizations and Applications [in Russian], Naukova Dumka, Kiev (1982), pp. 152–156.
S. R. Nasyrov, “On the application of the Loewner Kufarev equation to the determination of sufficient conditions for univalence,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 52–54 (1983).
S. R. Nasyrov and M. A. Sevodin, “Nehari-Pokornyi type univalence conditions in starshaped domains,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 78–80 (1981).
S. R. Nasyrov and Yu. E. Khokhlov, “The uniqueness of the solution of the exterior inverse boundary value problem in the class of spiral-shaped domains,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 24–27 (1984).
I. R. Nezhmetdinov, “Sufficient conditions for the univalence of the solution of an inverse problem of the theory of filtration in an inclined reservoir,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 15, 93–98 (1978).
I. R. Nezhmetdinov, “Sufficient conditions and radii of almost convexity of analytic functions,” Kazan. Univ., Kazan (1978). (Manuscript deposited at VINITI, Dec. 5, 1978, No. 3703 78 Dep.)
I. R. Nezhmetdinov, “Univalence tests for analytic functions and integral representations,” Kazan. Univ., Kazan (1978). (Manuscript deposited at VINITI, Dec. 12, 1978, No. 3764-78 Dep.)
I. R. Nezhmetdinov, “One-sided moduli of continuity and sharp estimates for harmonic functions,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 149–158 (1984).
M. T. Nuzhin, “On certain inverse boundary value problems and their application to the determination of the shape of the cross section of a twisted beam,” Uch Zap. Kazan. Univ.,109, No. 1, 97–120.
M. T. Nuzhin, “On the solution of the fundamental inverse problem and of problems reducing to it,” Uch. Zap. Kazan. Univ., 111, Book 8, 139–147 (1951).
M. T. Nuzhin, “On the formulation and the solution of inverse problems of forced filtration,” Dokl. Akad. Nauk SSSR,96, No. 4, 709–711 (1954).
M. T. Nuzhin and N. B. Il'inskii, Methods for the Determination of the Underground Contours of Hydrotechnic Constructions. Inverse Boundary Value Problems of Filtration Theory [in Russian], Kazan Univ. (1963).
M. T. Nuzhin and G. G. Tumashev, “Inverse boundary value problems and their application to mechanics,” in: Third All-Union Mathematical Congress (1956), Vol. 1 [in Russian], Academy of Sciences of the SSSR, Moscow (1956), pp. 208–209.
M. T. Nuzhin and G. G. Tumashev, “Inverse boundary value problems and their application to mechanics,” in: Third All-Union Mathematical Congress (1956), Vol. 3 [in Russian], Academy of Sciences of the SSSR, Moscow (1958), pp. 462–466.
M. T. Nuzhin and G. G. Tumashev, “Inverse boundary value problems and their application to fluid mechanics,” in: Second All-Union Congress on Theoretical and Applied Mechanics (1964). Abstract of Communications [in Russian], Moscow (1964), p. 162.
G. A. Pavlovets and N. D. Samoznaev, “A numerical method for the construction of the contour of the wing profile from the prescribed velocity surface on its surface. Tr. TsAGI, No. 1271 (1970).
P. S. Pankov and B. D. Bayachorova, “The application of demonstrative calculation on a computer for the construction of an example in the theory of univalent functions,” Redkollegiya Izv. Akad. Nauk KirgSSR, Frunze (1980). (Manuscript deposited at VINITI, Jan. 28, 1980, No. 341-80 Dep.)
E. L. Patsevich, “Estimates for functions harmonic in a circle, and their application to inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 11, 144–148 (1974).
E. L. Patsevich, “Estimates for harmonic functions, and their application to inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Razan. Univ., No. 12, 172–176 (1975).
E. L. Patsevich, “Sufficient conditions for univalence of certain integral representations,” Mat. Zametki,27, No. 3, 399–410 (1980).
V. V. Pokornyi, “On certain sufficient univalence conditions,” Dokl. Akad. Nauk SSSR,79, No. 5, 743–746 (1951).
G. Polya and G. Szego, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press (1951).
P. Ya. Polubarinova-Kochina, The Theory of Motion of Ground Water [in Russian], Nauka, Moscow (1977).
S. P. Ponomarev, “On the question of the AC-removability of quasiconformal curves,” Dokl. Akad, Nauk SSSR,227, No. 3, 566–568 (1976).
M. Popov, K. Varsamov, and Iv. Belberov, Izv. VMEI “Lenin”, No. 16, 92–95 (1975).
V. A. Pokhilevich, “On a theorem of M. Biernacki in the theory of univalent functions,” Ukr. Mat. Zh.,17, No. 4, 63–71 (1965).
I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow-Leningrad (1950).
I. I. Privalov, Introduction to the Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1960).
P. I. Pronin, “The univalence of hypergeometric operators,” in: Operators and Their Applications. The Approximation of Functions. Equations [in Russian], Leningrad (1985), pp. 66–71.
D. V. Prokhorov, “On a certain generalization of the class of almost convex functions,” Mat. Zametki,11, No. 5, 509–516 (1972).
D. V. Prokhorov, “On the geometric characterization of functions from Bazilevich subclasses,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 130–132 (1975).
D. V. Prokhorov, “Integrals of univalent functions,” Mat. Zametki,24, No. 5, 671–678 (1978).
D. V. Prokhorov, “Integral transformations in certain classes of univalent functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 45–49 (1980).
D. V. Prokhorov, “On a sufficient condition for univalence,” in: Differential Equations and Theory of Functions, No. 3 [in Russian], Saratov (1980), pp. 49–52.
D. V. Prokhorov, “Combined criteria for univalence of functions analytic in the disk,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 76–77 (1983).
D. V. Prokhorov, “On the properties of functions that satisfy the Becker condition,” in: Theory of Functions and Approximations. Interpolation, Geometric Theory of Functions [in Russian], Saratov State Univ. (1983), pp. 32–34.
D. V. Prokhorov, “On the ranges of systems of functionals and the integration of univalent functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 33–39 (1986).
D. V. Prokhorov and B. N. Rakhmanov, “On an integral representation of a certain class of univalent functions,” Mat. Zametki,19, No. 1, 41–48 (1976).
I. Radon (J. Radon), “On boundary value problems for the logarithmic potential,” Usp. Mat. Nauk,1, No. 1–2, 96–124 (1946).
B. N. Rakhmanov, “On the theory of univalent functions,” Dokl. Akad. Nauk SSSR,91, No. 4, 729–732 (1953).
B. N. Rakhmanov, “On the theory of univalent functions,” Dokl. Akad. Nauk SSSR,92, No. 6, 973–976 (1954).
B. N. Rakhmanov, “On certain classes of univalent functions,” in: Studies in Differential Equations and Theory of Functions, No. 3 [in Russian], Saratov State Univ. (1971), pp. 63–65.
Yu. A. Reshetnikov, “Sufficient conditions for the univalence of the solution of an inverse problem of hydrodynamics,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 10, 107–111 (1973).
Yu. A. Reshetnikov, “An inverse mixed problem of electrostatics,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 78–85 (1977).
Yu. A. Reshetnikov, “Sufficient conditions for the univalence of regular functions in a circular annulus,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 73–75 (1982).
Yu. G. Reshetnyak, Spatial Mappings with Bounded Distortion [in Russian], Nauka, Novosibirsk (1982).
V. S. Rogozhin, “Two sufficient conditions for the univalence of mappings,” Uch. Zap. Rostov.-na-Don Univ.,32, No. 4, 135–137 (1955).
V. S. Rogozhin, “An inverse problem of shock theory,” Uch. Zap. Kazan. Univ.,117, No. 2, 36–37 (1957).
V. S. Rogozhin, “On the uniqueness of the solution of the exterior inverse boundary value problem,” Uch. Zap. Kazan. Univ.,117, No. 2, 38–41 (1957).
V. S. Rogozhin, “Sufficient conditions for the univalence of the solutions of inverse boundary value problems,” Prikl. Mat. Mekh.,22, No. 6, 804–807 (1958).
V. S. Rogozhin, “On the number of solutions of an exterior inverse boundary value problem,” Uch Zap. Rostovsk. n/D Univ.,66, No. 7, 155–158 (1959).
V. S. Rogozhin, “Finding the shape of a body from a given impact pressure,” Prikl. Mat. Mekh.,23, No. 3, 589–591 (1959).
S. B. Sagitova, “Inverse boundary value problems with respect to the parameter in multiply connected domains,” Kazan. Univ., Kazan (1982). (Manuscript deposited at VINITI, Nov. 16, 1982, No. 5599-82 Dep.)
S. B. Sagitova and E. A. Shirokova, “An inverse boundary value problem for the parameter,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 19, 175–184 (1982).
R. B. Salimov, “Exterior inverse problems for the case when the boundary conditions are given as a function of the Cartesian coordinate x,” Uch. Zap. Kazan. Univ.,117, No. 9, 60–64 (1957).
R. B. Salimov, Some Fundamental Problems on the Variation of the Contours in the Theory of Analytic Functions and Their Application to Fluid Dynamics [in Russia], Izd. Kazan. Vyssh. Komandno-Inzhenernogo Uchilishcha (1970).
R. B. Salimov and Yu. M. Molokovich, “On the inverse problem of aerohydromechanics regarding the variation of profiles,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 150–157 (1963).
R. B. Salimov and M. L. Slavutin, “An inverse boundary value problem for infinitely connected domains,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 20, 192–200 (1983).
R. B. Salimov and M. L. Slavutin, “An inverse boundary value problem for the case of an infinite unknown contour,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 80–86 (1984).
R. B. Salimov and M. L. Slavutin, “An inverse boundary value problem for functions with pole and logarithmic singularity,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 180–186 (1984).
R. B. Salimov and M. L. Slavutin, ”An inverse boundary value problem for a lattice of infinite contours in the case of the parameter x,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 22, 178–183 (1985).
N. D. Samoznaev, “The construction of the lattice of profiles from the prescribed velocity distribution on their surfaces,” Tr. TsAGI, No. 1452 (1973), pp. 3–11.
N. D. Samoznaev, “The construction of the contour of a wing profile from the prescribed velocity distribution or from the pressure on its surface near the ground,” Tr. TsAGI, No. 1463 (1973).
M. A. Sevodin, “Some sufficient conditions for the univalence of the general solution of an inverse boundary value problem,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 18, 184–192 (1981).
M. A. Sevodin, “On sufficient conditions for thep-valence of analytic functions,” Kazan. Univ., Kazan (1981). (Manuscript deposited at VINITI, July 10, 1981, No. 3439–81 Dep.)
M. A. Sevodin and P. L. Shabalin, “On the refinement of the separating constants in the test for univalence of the solution of an inverse boundary value problem,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 17, 167–179 (1980).
M. A. Sevodin and P. L. Shabalin, “Univalence conditions for functions thar are regular in a circular annulus,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 19, 184–191 (1982).
L. A. Simonov, “The construction of profiles from the velocity hodograph,” Prikl. Mat. Mekh.,4, No. 4, 97–116 (1940).
L. A. Simonov, “The construction of profiles from the velocity hodograph,” Prikl. Mat. Mekh.,5, No. 2, 193–222 (1941).
M. L. Slavutin, “On the univalent solvability of an inverse boundary value problem for infinitely connected domains,” Kazan. Inzh.-Stroit. Inst., Kazan (1984). (Manuscript deposited at VINITI, Mar. 14, 1984, No. 1400-84 Dep.)
A. I. Slutskii, “The application of the source method for solving the problem of the flow around a symmetric profile and to the problem of the construction of a symmetric profile from a prescribed pressure distribution,” Tr. TsAGI, No. 663 (1948).
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press (1970).
G. Yu. Stepanov, Hydrodynamics of Turbines [in Russian], Fizmatgiz, Moscow (1962).
S. Stoilow, Lecons sur les Principes Topologiques de la Theorie des Fonctions Analytiques, Gauthier-villars, Paris (1956).
R. M. Timerbaev, “On symmetric solutions of the inverse problem of hydromechanics,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 13, 239–245 (1976).
A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems (2nd revised edition [in Russian], Nauka, Moscow (1979).
A. P. Tikhonov, “Some sufficient conditions for the univalence of meromorphic functions,” Redkollegiya Zh. Izv. Vuzov. Mat., Kazan (1980). (Manuscript deposited at VINITI, May 5, 1980, No. 1769-80 Dep.)
A. P. Tikhonov, “On the theory of the univalence of the solution of the exterior inverse boundary value problem,” Rostov n/D Univ., Rostov-on-the-Don (1981). (Manuscript deposited at VINITI, Jan. 29, 1981, No. 400-81 Dep.)
A. P. Tikhonov, “On the univalent solvability of an exterior inverse boundary value problem,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 85–87 (1981).
A. P. Tikhonov and Yu. E. Khokhlov, “Biholomorphy of solutions of the inverse boundary value problem in Cn,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 16, 163–179 (1979).
Yu. Yu. Trokhimchuk, Continuous Mappings and Conditions for Mogoneity, Israel Program for Scientific Translations, Jerusalem (1964).
G. G. Tumashev, “The determination of the shape of the boundary of the flow of a fluid from a prescribed distribution of velocities or pressures,” Uch. Zap. Kazan. Univ.,112, No. 3, 3–24 (1952).
G. G. Tumashev, “The problem of constructing a doubly periodic hydrodynamic lattice from a velocity distribution,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 194–197 (1974).
G. G. Tumashev and M. T. Nuzhin, “Inverse boundary value problems,” Uch. Zap. Kazan. Univ.,115, No. 6 (1955).
G. G. Tumashev and M. T. Nuzhin, Inverse Boundary Value Problems and Their Applications [in Russian], Kazan State Univ. (1965).
G. G. Tumashev and M. T. Nuzhin, “Inverse boundary value problems,” in: Abstracts of Short Communications at the International Congress of Mathematicians, Section 12, Moscow (1966), p. 53.
W. K. Hayman, Multivalent Functions, Cambridge Univ. Press (1958).
Yu. E. Khokhlov, “Operators and operations on the class of univalent functions,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 83–89 (1978).
Yu. E. Khokhlov, “The city seminar on the geometric theory of function at the Kazan State University,” Usp. Mat. Nauk,33, No. 1, 251–252 (1978).
Yu. E. Khokhlov, “On Mocanu and Bazilevich functions of several complex variables,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 15, 132–138 (1978).
Yu. E. Khokhlov, “Parametric families of biholomorphic mappings,” in: Theory of Mappings, Its Generalizations and Applications [in Russian], Naukova Dumka, Kiev (1982), pp. 221–225.
Yu. E. Khokhlov, “On the solvability of problems with free boundaries for analytic functions in unbounded domains,” in: Abstracts of the Reports of the Republican Conference on Nonlinear Problems of Mathematical Physics [in Russian], Donetsk (1983), p. 135.
Yu. E. Khokhlov, “Hadamard convolution, hypergeometric functions and linear operators in the class of univalent functions,” Dokl. Akad. Nauk Ukrain. SSR, Ser. A, No. 7, 25–27 (1984).
Yu. E. Khokhlov, “On the solvability of exterior inverse boundary value problems for analytic functions,” Dokl. Akad. Nauk SSSR,278, No. 2, 298–301 (1984).
Yu. E. Khokhlov, “Convolution operators that preserve univalent functions,” Ukr. Mat. Zh.,37, No. 2, 220–226 (1985).
Yu. E. Khokhlov and V. A. Tsapov, “Linear operators and imbedding theorems for certain classes of univalent functions,” in: Theory of Mappings and Approximation of Functions [in Russian], Naukova Dumka, Kiev (1983), pp. 110–117.
V. G. Cherednichenko, “Univalent functions and the inverse potential problem,” Dokl. Akad. Nauk SSSR,264, No. 1, 48–51 (1982).
V. G. Cherednichenko, “Continuation with respect to a parameter of the solution of a two-dimensional inverse problem of the potential,” Dokl. Akad. Nauk SSSR,268, No. 2, 299–302 (1983).
A. V. Chernavskii, “Addendum to the paper “On finitely multiple mappings of manifolds”, Mat. Sb.,66 (108), No. 3, 471–472 (1965).
L. I. Chibrikova, Fundamental Boundary Value Problems for Analytic Functions [in Russian], Kazan. Univ., Kazan (1977).
P. L. Shabalin, “On the univalence of the general solution of an interior inverse boundary value problem,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 92–95 (1975).
P. L. Shabalin, “On the univaience of the solution of the exterior inverse boundary value problem,” Kazan. Univ., Kazan (1976). (Manuscript deposited at VINITI, July 14, 1976, No. 2657-76 Dep.)
P. L. Shabalin, “Univalence classes and V. I. Smirnov's domains,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 16, 218–226 (1979).
P. L. Shabalin, “On certain characteristics of univalent solutions of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 210–216 (1984).
E. A. Shirokova, “Certain questions on the univalence of functions of class ⌆,”e Mat. Zametki,18, No. 3, 403–410 (1975).
E. A. Shirokova, “On the application of the area method to the construction of parametric families of univalent functions,” Kazan. Univ., Kazan (1977). (Manuscript deposited at VINITI, May 5, 1977, No. 1792-77 Dep.)
E. A. Shirokova, “On the univalence of certain integrals,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 107–114 (1977).
E. A. Shirokova, “On the extension of the subclass of Bazilevich functions and on the properties of the Bernardi integral,” Kazan. Univ., Kazan (1977). (Manuscript deposited at VINITI, Sep. 9, 1977, No. 3623-77 Dep.)
E. A. Shirokova, “On the univalence of solutions of interior inverse boundary value problems in the case of the parametersx andr,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 15, 185–190 (1978).
E. A. Shirokova, “Some questions on the univalence of solutions of inverse boundary value problems,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 90–94 (1978).
E. A. Shirokova, “Application of homotopic families of closed curves for the study of the univalence of the solution of inverse boundary value problems,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 16, 235–239 (1979).
E. A. Shirokova, “On some operators that do not lead out of the class of functions univalent in the disk,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 66–72 (1984).
E. A. Shirokova, “Application of Fredholm integral equations in the investigation of an interior inverse boundary value problem,” Trudy Sem. Kraev. Zadacham, Kazan. Univ., No. 21, 233–239 (1984).
L. V. Ahlfors, “Quasiconformal reflections,” Acta Math.,109, 291–301 (1963).
L. V. Ahlfors, “Sufficient conditions for quasiconformal extension,” in: Discontinuous Groups and Riemann Surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), Ann. of Math. Studies, No. 79, Princeton Univ. Press (1974), pp. 23–29.
L. Ahlfors and G. Weill, “A uniqueness theorem for Beltrami equations,” Proc. Am. Math. Soc,13, No. 6, 975–978 (1962).
L. A. Aksentijev, N. B. Ilyinski, M. T. Nuzhin, R. B. Salimov, and G. G. Tumashev, “The inverse boundary-value problems theory in the continuum mechanics,” in: Theor. and Appl. Mech. 14th IUTAM Congr., Delft, 1976, Abstracts, Amsterdam (1976), p. 46.
H. Al-Amiri and P. T. Mocanu, “Certain sufficient conditions for univalency of the class C′,” J. Math. Anal. Appl.,80, No. 2, 387–392 (1981).
H. Al-Amiri and P. T. Mocanu, “Spirallike nonanalytic functions,” Proc. Am. Math. Soc.,82, No. 1, 61–65 (1981).
J. M. Anderson and A. Hinkkanen, “Univalent functions and domains bounded by quasicircles,” J. London Math. Soc.,25, No. 2, 253–260 (1982).
J. M. Anderson and A. Hinkkanen, “A univalency criterion,” Michigan Math. J.,32, No. 1, 33–40 (1985).
B. Arlinger, An exact method of two-dimensional airfoil design. TN 67, Oct., 1970, SAAB, Linkoping, Sweden.
A. Baernstein II, “Integral means, univalent functions and circular symmetrization,” Acta Math.,133, 139–169 (1975).
S. K. Bajpai, “Special arithmetic and geometric means preserve Φ-like univalence,” Rev. Colombiana Mat.,12, No. 3–4, 83–90 (1978).
A. F. Beardon and F. W. Gehring, “Schwarzian derivatives, the Poincaré metric and the kernel function,” Comment. Math. Helv.,55, No. 1, 50–64 (1980).
J. Becker, “Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen,” J. Reine Angew. Math.,255, 23–43 (1972).
J. Becker, “über homöomorphe Fortsetzung schlicnter Funktionen,” Ann. Acad. Sci. Fenn. Ser. A I, No. 538 (1973).
J. Becker, “Löwnersche Differentialgleichung und Schlichtheitskriterien,” Math. Ann.,202, No. 4, 321–335 (1973).
J. Becker and Ch. Pommerenke, “über die quasikonforme Fortsetzung schlichter Funktionen,” Math. Z.,161, 69–80 (1978).
J. Becker and Ch. Pommerenke, “Schlichtheitskriterien und Jordangebiete,” J. Reine Angew. Math.,354, 74–94 (1984).
P. R. Beesack, “Nonoscillation and disconjugacy in the complex domain,” Trans. Am. Math. Soc,81, No. 1, 211–242 (1956).
S. D. Bernardi, “A survey of the development of the theory of schlicht functions,” Duke Math. J.,19, No. 2, 263–287 (1952).
A. Bielecky and Z. Lewandowski, “Sur un theoreme concernant les fonctions univalentes lineairement accessibles de M. Biernacki,” Ann. Polon. Math.,12, No. 1, 61–63 (1962).
M. Biernacki, Les Fonctions Multivalents, Gauthier-villars, Paris (1938).
M. Biernacki, “Sur l'intégrale des fonctions univalentes,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys.,8, No. 1, 29–34 (1960).
L. de Branges, “A proof of the Bieberbach conjecture,” Acta Math.,154, No. 1–2, 137–152 (1985).
L. Brickman, “Φ-like analytic functions. I,” Bull. Am. Math. Soc.,79, No. 3, 555–558 (1973).
D. R. Bristow, “A new surface singularity method for multielement airfoil analysis and design,” AIAA Pap., No. 20, 1976.
J. E. Brown, “Some sharp neighborhoods of univalent functions,” Trans. Am. Math. Soc.,287, No. 2, 475–482 (1985).
D. M. Campbell and V. Singh, “Valence properties of the solution of a differential equation,” Pac. J. Math.,84, No. 1, 29–33 (1979).
B. A. Case and J. R. Quine, “Conditions for some polygonal functions to be Bazilevic,” Proc. Am. Math. Soc.,88, No. 2, 257–261 (1983).
W. M. Causey, “The close-to-convexity and univalence of an integral,” Math. Z.,99, No. 3, 207–212 (1967).
W. M. Causey and M. O. Reade, “On the univalence of functions defined by certain integral transforms,” J. Math. Anal. Appl.,89, No. 1, 28–39 (1982).
W. M. Causey and W. L. White, “Starlikeness of certain functions with integral representations,” J. Math. Anal. Appl.,64, 458–466 (1978).
R. N. Das and P. Singh, “On subclasses of schlicht mapping,” Indian J. Pure Appl. Math.,8, No. 8, 864–872 (1977).
P. L. Duren and O. Lehto, “Schwarzian derivatives and homeomorphic extensions,” Ann. Acad. Sci. Fenn. Ser. A I, No. 477 (1970).
P. L. Duren, H. S. Shapiro, and A. L. Shields, “Singular measures and domains not of Smirnov type,” Duke Math. J.,33, No. 2, 247–254 (1966).
U. Elias, “Nonoscillation theorems in convex sets,” J. Math. Anal. Appl.,52, No. 1, 129–141 (1975).
R. Eppler, “Direkte Berechnung von Tragflugelprofilen aus der Druckwerteilung,” Ing.-Arch.,25, No. 1, 32–57 (1957).
M. Fait, J. G. Krzyz, and J. Zygmunt, “Explicit quasiconformal extensions for some classes of univalent functions,” Comment. Math. Helv.,51, No. 2, 279–285 (1976).
C. H. Fitzgerald and Ch. Pommerenke, “The de Branges theorem on univalent functions,” Trans. Am. Math. Soc.,290, No. 2, 683–690 (1985).
S. Friedland and Z. Nehari, “Univalence conditions and Sturm-Liouville eigenvalues,” Proc. Am. Math. Soc.,24, No. 3, 595–603 (1970).
F. W. Gehring, “Univalent functions and the Schwarzian derivative,” Comment. Math. Helv.,52, No. 4, 561–572 (1977).
F. W. Gehring and B. G. Osgood, “Uniform domains and the quasi-hyperbolic metric,” J. Analyse Math.,36, 50–74 (1979).
F. W. Gehring and Ch. Pommerenke, “On the Nehari univalence criterion and quasicircles,” Comment. Math. Helv.,59, No. 2, 226–242 (1984).
J. Gevirtz, “An upper bound for the John constant,” Proc. Am. Math. Soc,83, No. 3, 476–478 (1981).
J. Gevirtz, “Onf″/f′ and injectivity,” Ann. Acad. Sci. Fenn. Ser. A I Math.,8, No., 1, 87–92 (1983).
R. M. Goel and N. S. Sohi, “On the order of starlikeness of a subclass of convex functions and some convolution results,” Houston J. Math.,9, No. 2, 209–216 (1983).
A. W. Goodman, “On the Schwarz-Christoffel transformation and p-valent functions,” Trans. Am. Math. Soc.,68, No. 2, 204–223 (1950).
A. W. Goodman, “A note on the Noshiro-Warschawski theorem,” J. Analyse Math.,25, 401–408 (1972).
A. W. Goodman, “The domain of univalence of certain families of rational functions,” Proc Am. Math. Soc.,66, No. 1, 85–90 (1977).
A. W. Goodman, “Remarks on the Schwarz-Christoffel transformation,” in: E. B. Christoffel (Aachen/Monschau, 1979), Birkhauser, Basel (1981), pp. 253–262.
D. J. Hallenbeck and A. E. Livingston, “A coefficient estimate for multivalent functions,” Proc Am. Math. Soc.,54, No. 1, 201–206 (1976).
R. Harmelin, “Bergman kernel function and univalence criteria,” J. Analyse Math.,41, 249–258 (1982).
R. Harmelin, “Aharonov invariants and univalent functions,” Israel J. Math.,43, No. 3, 244–254 (1982).
W. K. Hayman, “Research problems in function theory,” in: Symposium on Complex Analysis (Canterbury, 1973), London Math. Soc. Lecture Note Series, No. 12, Cambridge Univ. Press, Cambridge (1974), pp. 143–154.
F. Herzog and G. Piranian, “On the univalence of functions whose derivative has a positive real part,” Proc, Am. Math. Soc,2, No. 4, 625–633 (1951).
E. Hille, “Remarks on a paper by Zeev Nehari,” Bull. Am. Math. Soc.,55, No. 6, 552–553 (1949).
Z. J. Jakubowski and J. Kaminski, “On some properties of Mocanu Janowski functions,” Rev. Roumaine Math. Pures Appl.,23, No. 10, 1523–1532 (1978).
F. John, “A criterion for univalency brought up to date,” Commun. Pure Appl. Math.,29, No. 3, 293–295 (1976).
D. Y. Jones and S. Eggleston, “On the design of modern airfoils sections by numerical methods,” in: Innovative Numer. Anal. Eng. Sci. Proc., 2nd Internat. Symp., Montreal, 1980, Charlottesviile (1980), pp. 169–178.
W. Kaplan, “Close-to-convex schlicht functions,” Michigan Math. J.,1, No. 2, 169–185 (1952).
J. L. Kennedy and D. J. Marsden, “A potential flow design method for multicomponent airfoil sections,” J. Aircraft,15, No. 1, 47–52 (1978).
J. G. Krzyz, “Convolution and quasiconformal extension,” Comment. Math. Helv.,51, No. 1, 99–104 (1976).
J. Krzyz, “über schlichte quasikonform fortsetzbare Funktionen,” Wiss. Beitr. Martin-Luther-Univ. Halle-Wittenberg, M, No. 9, 33–35 (1977).
J. Krzyz and Z. Lewandowski, “On the integral of univalent functions,” Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys.,11, No. 7, 447–448 (1963).
R. Kühnau, “Zur quasikonformen Fortsetzbarkeit schlichter konformer Abbildungen,” Bull. Soc. Sci. Lettres Llodz,26, No. 6, 1–4 (1974, 1975).
R. Kühnau and H. Blaar, “Kriterien fur quasikonforme Fortsetzbarkeit konformer Abbildungen eines Kreisringes bzw. des Inneren oder Ausseren einer Ellipse,” Math. Nachr.,91, 183–196 (1979).
V. Kumar, “On a new criterion for univalent functions,” Demonstratio Math.,17, No. 4, 875–886 (1984).
R. J. Leach, “Multivalent and meromorphic functions of bounded boundary rotation,” Can. J. Math.,27, No. 1, 186–199 (1975).
R. J. Leach, “Multivalent Bazilevic functions,” Rev. Roumaine Math. Pures Appl.,21, No. 5, 523–527 (1976).
M. Lehtinen, “On the inner radius of univalency for noncircular domains,” Ann. Acad. Sci. Fenn. Ser. A I Math., 5, No. 1, 45–47 (1980).
O. Lehto, “On univalent functions with quasiconformal extensions over the boundary,” J. Analyse Math.,30, 349–354 (1976).
O. Lehto, “Domain constants associated with Schwarzian derivative,” Comment. Math. Helv.,52, No. 4, 603–610 (1977).
O. Lehto, “Univalent functions, Schwarzian derivatives and quasiconformal mappings,” Enseign. Math.24, No. 34, 203–214 (1978).
O. Lehto, “Remarks on Nehari's theorem about the Schwarzian derivative and schlicht functions,” J. Analyse Math.,36, 184–190 (1979).
O. Lehto and O. Tammi, “Schwarzian derivative in domain of bounded boundary rotation,” Ann. Acad. Sci. Fenn. Ser. A I Math.,4, No. 2, 253–257 (1978/79).
H. Levi, “über die Darstellung ebener Kurven mit Doppelpunkten,” Nachr. Akad. wiss. Gottingen II: Math. Phys. Kl., No. 4, 109–130 (1981).
A. E. Livingston, “p-valent close-to-convex functions,” Trans. Am. Math. Soc.,115, 161–179 (1965).
Z. Lewandowski, “Some remarks on univalence criteria,” Ann. Univ. Mariae Curie-Sklodowska, Sec. A,36–37, 87–95 (1982–83).
Z. Lewandowski, “Some remarks on univalence criteria for functions meromorphic in the exterior of the unit disc,” Ann. Polon. Math.,46, 177–181 (1985).
Z. Lewandowski and J. Stankiewicz, “Univalence conditions and conditions for quasicon-formal extensions,” Wiss. Beitr. Martin-Luther-Univ. Halle-Wittenberg, M, No. 35, 44–47 (1984).
R. J. Libera, “Some classes of regular univalent functions,” Proc. Am. Math. Soc.,16, No. 4, 755–758 (1965).
R. H. Liebeck, “Design of subsonic airfoils for high lift,” J. Aircraft,15, No. 9, 547–561 (1978).
R. H. Liebeck, “A class of airfoils designed for high lift in incompressible flow,” J. Aircraft,10, No. 10, 610–617 (1973).
R. H. Liebeck and A. I. Ormsbee, “Optimization of airfoils for maximum lift,” J. Aircraft,7, No. 5, 409–415 (1970).
M. J. Lighthill, “A mathematical method of cascade design,” Aeronaut. Res. Counc. Repts. and Mem., No. 2014 (1945).
D. London, “On the zeros of the solutions ofw′ (z) + p(z)w(z) = 0,” Pac. J. Math.,12, No. 3, 979–991 (1962).
A. Lyzzaik, “Multivalent functions of bounded boundary rotation and weakly close-toconvex functions,” Proc. London Math. Soc.51, No. 3, 478–500 (1985).
W. Mangier, “Die Berechnung eines Tragflügelprofiles mit vorgeschriebener Druckverteilung,” Jahrb. der Deutsch. Luftfahrtforschung, 146-153 (1938).
O. Martio and J. Sarvas, “Injectivity theorems in plane and space,” Ann. Acad. Sci. Fenn. Ser. A I Math.,4, No. 2, 383–401 (1979).
E. P. Merkes, “Univalence of an integral transform,” Contemp. Math.,38, 113–119 (1985).
S. S. Miller, P. Mocanu, and M. O. Reade, “Allα-convex functions are univalent and starlike,” Proc. Am. Math. Soc.,37, No. 2, 553–554 (1973).
S. S. Miller, P. T. Mocanu, and M. O. Reade, “Starlike integral operators,” Pac. J. Math.,79, No. 1, 157–168 (1978).
D. Minda, “The Schwarzian derivative and univalence criteria,” Contemp. Math.,38, 43–52 (1985).
P. T. Mocanu, “Starlikeness and convexity for nonanalytic functions in the unit disk,” Mathematica (Cluj),22 (45), No. 1, 77–83 (1980).
P. T. Mocanu, “Sufficient conditions of univalency for complex functions in the class C1,” Anal. Numer. Theor. Approx.,10, No. 1, 75–79 (1981).
P. Montel, LeÇons sur les Fonctions Univalentes ou Multivalentes, Gauthier-Villars, Paris (1933).
E. J. Moulis, Jr., “The univalence of a class of analytic functions,” in: Complex Analysis (Proc. SUNY Conf., Brockport, N.Y., 1976), Dekker, New York (1978), pp. 89–94.
J. C. Narramore, “An approach to subsonic turbulent flow airfoil design using minicomputers,” SAE Preprint, No. 770479 (1977).
Z. Nehari, “The Schwarzian derivative and schlicht functions,” Bull. Am. Math. Soc.,55, No. 6, 545–551 (1949).
Z. Nehari, “Some criteria of univalence,” Proc. Am. Math. Soc.,5, 700–704 (1954).
Z. Nehari, “Conformal invariants and linear differential equations,” in: Seminars on Analytic Functions, Vol. I, Inst. Advanced Study, Princeton (1958), pp. 289–301.
Z. Nehari, “A property of convex conformal maps,” J. Analyse Math.,30, 390–393 (1976).
Z. Nehari, “Univalence criteria depending on the Schwarzian derivative,” Illinois J. Math.,23, No. 3, 345–351 (1979).
J. W. Noonan, “Powers ofp-valent functions,” J. Austral. Math. Soc.,A25, No. 1, 66–70 (1978).
K. Noshiro, “On the theory of schlicht functions,” J. of the Faculty of Science, Hokkaido Imp. Univ.,2, 124–155 (1934).
M. Nunokawa, “On the Bazilevic analytic functions,” Sci. Rep. Fac. Ed. Gumma Univ.,21, 9–31 (1972).
M. Nunokawa, “On the Bazilevic analytic functions. II,” Sci. Rep. Fac. Ed. Gumma Univ.,22, 13–16 (1973).
M. Nunokawa, “A class of multivalent functions,” Sci. Rep. Fac. Ed. Gumma Univ.,23, 11–15 (1974).
M. Nunokawa, “An application of Ruscheweyh's univalence condition,” Sci. Rep. Fac. Ed. Gumma Univ.,26, 23–26 (1977).
A. I. Ormsbee and A. W. Chen, “Multiple element airfoils optimized for maximum lift coefficient,” AIAA J.,10, No. 12, 1620–1624 (1972).
B. G. Osgood, “Univalence criteria in multiply-connected domains,” Trans. Am. Math. Soc,260, No. 2, 459–473 (1980).
B. G. Osgood, “Some properties off″/f′ and the Poincaré metric,” Indiana Univ. Math. J.,31, No. 4, 449–461 (1982).
A. Ostrowski, “Un critère d'univalence des transformations dans unR n,” C. R. Acad. Sci. Paris,247, No. 2, 172–175 (1958).
A. Ostrowski, “Un nouveau critère d'univalence des transformations dans unR n” C. R. Acad. Sci. Paris,248, No. 3, 348–350 (1959).
S. Owa, “A remark on new criteria for univalent functions,” Kyungpook Math. J.,21, No. 1, 15–23 (1981).
S. Owa, “On the Ruscheweyh's new criteria for univalent functions,” Math. Japon.,27, No. 1, 77–96 (1982).
S. Owa, “On new criteria forp-valent functions,” Indian J. Pure Appl. Math.,13, No. 8, 920–930 (1982).
S. Owa, “A class of analyticp-valent functions,” Math. Japon.,28, No. 1, 73–81 (1983).
S. Owa, “On new criteria for univalent functions,” Tamkang J. Math.,15, No. 1, 25–34 (1984).
S. Ozaki and M. Nunokawa, “The Schwarzian derivative and univalent functions,” Proc. Am. Math. Soc.,33, No. 2, 392–394 (1972).
V. Paatero, über die konforme Abbildung von Gebieten, deren RÄnder von beschrÄnkter Drehung sind,” Akad. Abh. Helsinki, 1931.
K. S. Padmanabhan and R. Paryatham, “On functions with bounded boundary rotation,” Indian J. Pure Appl. Math.,6, No. 11, 1236–1247 (1975).
T. Parthasarathy, On Global Univalence Theorems, Lecture Notes in Math., No. 977, Springer, Berlin (1983).
N. N. Pascu, “On Rahmanov's theorem,” Bull. Univ. Brasov,24, 25–26 (1982).
J. A. Pfaltzgraff, “Quasiconformal extension of holomorphic mappings of a ball inC n,” Bull. Am. Math. Soc.,80, 543–544 (1974).
J. A. Pfaltzgraff, “Subordination chains and quasiconformal extension of holomorphic maps in Cn,” Ann. Acad. Sci. Fenn. Ser. A I Math.,1, No. 1, 13–25 (1975).
Ch. Pommerenke, “über die Subordination analytischer Funktionen,” J. Reine Angew. Math.,218, 159–173 (1965).
Ch. Pommerenke, “Schlichte Funktionen und analytische Funktionen von beschrÄnkter mittlerer Oszillation,” Comment. Math. Helv.,52, No. 4, 591–602 (1977).
E. M. Popa, “Some sufficient conditions of univalency for complex functions of the class C1,” Lecture Notes in Math., No. 1013, 350–355 (1983).
M. O. Reade, “On Umezawa's criteria for univalence,” J. Math. Soc. Jpn.,9, No. 2, 234–238 (1957).
M. O. Reade, “On Umezawa's criteria for univalence. II,” J. Math. Soc. Jpn.,10, No. 3, 255–259 (1958).
M. O. Reade, “On Ogawa's criterion for univalence,” Publ. Math. Debrecen,11, No. 1–4, 39–43 (1964).
M. O. Reade and P. G. Todorov, “The radii of starlikeness of order alpha of certain Schwarz analytic functions,” Nauchn. Tr., Plovdiv. Univ.,21, No. 1, 87–92 (1983).
Q. I. Rahman and J. Szynal, “On some classes of univalent polynomials,” Can. J. Math.,30, No. 2, 332–349 (1978).
M. S. Robertson, “Complex powers ofp-valent functions and subordination,” in: Complex Analysis (Proc. SUNY Conf., Brockport, N.Y., 1976), Dekker, New York (1978), pp. 1–33.
M. S. Robertson, “A distortion theorem for analytic functions,” Proc. Am. Math. Soc.,28 No. 2, 551–556 (1971).
St. Ruscheweyh, “New criteria for univalent functions,” Proc. Am. Math. Soc,49, No. 1, 109–115 (1975).
St. Ruscheweyh, “A subordination theorem for Φ-like functions,” J. London Math. Soc.,13, No. 2, 275–280 (1976).
St. Ruscheweyh, “An extension of Becker's univalence condition,” Math. Ann.,220, 285–290 (1976).
C. Ryll-Nardzewski, “Une extension d'un theoreme de Sturm aux fonctions analytiques,” Ann. Univ. Mariae Curie-Sklodowska, Sect. A,4, 5–7 (1950).
J. Sato, “An exact two-dimensional incompressible potential flow theory of airfoil design with specified velocity distributions,” Trans. Jpn. Soc. Aeronaut. and Space Sci.,9, No. 14, 11–18 (1966).
G. Schober, Univalent Functions — Selected Topics, Lecture Notes in Math., No. 478, Springer, Berlin (1975).
B. Schwartz, “Complex nonoscillation theorems and criteria of univalence,” Trans. Am. Math. Soc.,80, No. 1, 159–186 (1955).
B. Schwartz, “On two univalence criteria of Nehari,” Illinois J. Math.,22, No. 2, 346–351 (1983).
T. Shell-Small, “On Bazilevic functions,” Quart. J. Math.,23, No. 90, 135–142 (1972).
T. B. Shell-Small, “Some linear operators in function theory,” in: Proc. Symp. on Complex Analysis (Univ. Kent, Canterbury, 1973), London Math. Soc. Lecture Note Ser., No. 12, Cambridge Univ. Press, London (1974), pp. 119–123.
V. Singh and P. N. Chichra, “An extension of Becker's criterion of univalence,” J. Indian Math. Soc.,41, No. 3–4, 353–361 (1977).
R. Singh and S. Singh, “Some sufficient conditions for univalence and starlikeness,” Colloq. Math.,47, No. 2, 309–314 (1982).
A. M. O. Smith, “High-lift aerodynamics,” J. Aircraft,12, No. 6, 501–530 (1975).
N. Steinmetz, “Locally univalent functions in the unit disk,” Ann. Acad. Sci. Fenn. Ser. A I Math.,8, No. 2, 325–332 (1983).
T. Strand, “Exact method of designing airfoil with given velocity distribution in incompressible flow,” J. Aircraft,10, No. 11, 651–659 (1973).
T. J. Suffridge, “Some remarks on convex maps of the unit disk,” Duke Math. J.,37, No. 4, 775–777 (1970).
T. J. Suffridge, “The principle of subordination applied to functions of several variables,” Pac. J. Math.,33, No. 1, 241–248 (1970).
T. Takatsuka, “Multivalent functions starlike in one direction,” Trans. Am. Math. Soc.,120, No. 1, 72–82 (1965).
S. R. Tims, “A theorem of functions schlicht in convex domains,” Proc. London Math. Soc.,1, No. 2, 200–205 (1951).
C. J. Titus, “The combinatorial topology of analytic functions on the boundary of a disk,” Acta Math.,106, No. 1, 45–64 (1961).
P. Todorov, “Maximal univalent mappings with bounded rotation that are realized by the class of integrals of Schwarz-Christoffel type,” Plovdiv. Univ. Nauchn. Trud.12, No. 1, 49–58 (1974).
P. G. Todorov, “Two simple proofs of the theorem for the maximal domain of univalence of the class of rational functions with simple poles and positive residues,” C. R. Acad. Bulgare Sci.,37, No. 4, 429–432 (1984).
T. Umezawa, “On the theory of univalent functions,” Tohoku Math. J.,7, No. 3, 213–228 (1955).
I. Wajnberg, “The theorem converse to J. A. Pfaltzgraff's theorem,” Zeszyty Nauk. Politech. Lodz. Mat., No. 18, 89–97 (1985).
S. E. Warschawski, “On the higher derivatives at the boundary in conformal mapping,” Trans. Am. Math. Soc.,38, 310–340 (1935).
J. Wolff, “L'intégrale d'une fonction holomorphe et a partie reelle positive dans un demi-plan est univalente,” C. R. Acad. Sci. Paris,198, No. 13, 1209–1210 (1934).
S. Yamashita, “On the John constant,” Math. Z.,161, No. 2, 185–188 (1978).
S. Yamashita, “Inequalities for the Schwarzian derivative,” Indiana Univ. Math. J.,28, No. 1, 131–135 (1979).
S. Yamashita, “On a theorem of Duren, Shapiro and Shields,” Proc. Am. Math. Soc.,73, No. 2, 180–182 (1979).
S. Yamashita, “Hardy norm, Bergman norm, and univalency,” Ann. Polon. Math.,43, No. 1, 23–33 (1983).
S. Yamashita, “On quasiconformal extension,” Ann. Univ. Mariae Curie-Sklodowska Sect. A,34, 103–106 (1980).
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 25, pp. 3–121, 1987.
Rights and permissions
About this article
Cite this article
Avkhadiev, F.G., Aksent'ev, L.A. & Elizarov, A.M. Sufficient conditions for the finite-valence of analytic functions and their applications. J Math Sci 49, 715–799 (1990). https://doi.org/10.1007/BF02207024
Issue Date:
DOI: https://doi.org/10.1007/BF02207024