Literature cited
G. G. Tumashev and M. T. Nuzhin, Converse Boundary Value Problems and Their Applications [in Russian], Kazan Univ. (1965).
F. D. Gakhov, Boundary Value Problems, Pergamon Press (1966).
N. P. Korneichuk, “On extremal properties of periodic functions,” Dopovidi Akad. Nauk Ukr. SSR,8, 993–998 (1962).
V. F. Storchai, “Exact estimates for norms of differentiable periodic functions in metric of L2,” Ukr. Mat. Zh.,25, No. 6, 835–841 (1973).
N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).
F. G. Avkhadiev and V. N. Gaiduk, “Application of almost convex functions to converse boundary value problems,” Izv. Vyssh. Uchebn. Zaved., Mat.,6, 3–10 (1968).
V. Paatero, Über die konforme Abbildung von Gebieten, deren Ränder von beschränkter Drehung sind, Helsinki (1931).
V. N. Gaiduk, “Some conditions for univalence of solution of converse boundary value problem for an n-symmetric function,” Proceedings of Seminar on Boundary Value Problems, Kazan Univ.,8, 55–58 (1971).
L. A. Aksent'ev, F. G. Avkhadiev, and V. P. Mikka, “New univalence tests and their application to converse boundary value problems,” Abstracts of Papers to Third Republican Mathematical Conference of Belorussia, Part 1, 79–80, Minsk (1971).
M. T. Nuzhin, “Solution of converse boundary value problem for doubly connected domain,” Uch. Zap. Kazansk. Univ.,110, 31–37 (1950).
L. A. Aksent'ev, V. N. Gaiduk, and V. P. Mikka, “Univalence criteria for n-symmetric functions,” Izv. Vyssh. Uchebn. Zaved., Mat.,4, 3–13 (1974).
E. L. Patsevich, “Estimates for harmonic functions and their application to converse boundary value problems,” Proceedings of Seminar on Boundary Value Problems, Kazan Univ.,12, 172–176 (1975).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 27, No. 3, pp. 399–410, March, 1980.
The author thanks L. A. Aksent'ev for his interest.
Rights and permissions
About this article
Cite this article
Patsevich, E.L. Sufficient conditions for univalence of some integral representations. Mathematical Notes of the Academy of Sciences of the USSR 27, 199–205 (1980). https://doi.org/10.1007/BF01140167
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01140167