This is a preview of subscription content, log in via an institution to check access.
Literature cited
P. T. Mocanu, “Une propriété de convexité generalisée dans la théorie de la re répresentation conforme,” Mathematiea (R. S. R.),11, No. 1, 127–133 (1969).
P. T. Mocanu and M. O. Reade, “On generalized convexity in conformai mappings,” Rev. Roumaine Math. Pures Appl.,16, No. 10, 1541–1544 (1971).
S. S. Miller, P. T. Mocanu, and M. O. Reade, “All α-convex functions are starlike,” Rev. Roumaine Math. Pures Appl.,17, No. 9, 1395–1397 (1972).
S. S. Miller, P. T. Mocanu, and M. O. Reade, “All α-convex functions are univalent and starlike,” Proc. Am. Math. Soc.,37, No. 2, 553–554 (1973).
V. A. Zmorovich and A. A. Yakubenko, “On a generalization of the class of α-convex functions of Mocanu,” in: Collected Papers in Mathematics [in Russian], Naukova Dumka, Kiev (1976), pp. 254–257.
V. A. Zmorovich and I. K. Korobkova, “On the order of starness of the class of α-convex functions for α ≤ −2,” in: Collected Papers in Mathematics [in Russian], Naukova Dumka, Kiev (1978), pp. 63–66.
V. A. Zmorovich and V. A. Pokhilevich, “On α-convex functions for α < 0,” Ukr. Mat. Zh.,31, No. 4, 431–433 (1979).
S. K. Bajpai, “On regions of α-convexity for starlike functions,” Proc. Am. Math. Soc.,44, No. 2, 365–368 (1974).
P. T. Mocanu and M. O. Reade, “The radius of α-convexity for the class of starlike univalent functions, α real,” Rev. Roumaine Math. Pure Appl.,20, No. 5, 561–565 (1975).
V. V. Chernikov and K. I. Sizhuk, “Some extremal problems in subclasses of starlike functions,” Sib. Mat. Zh.,19, No. 1, 193–200 (1978).
V. A. Pokhilevich and V. A. Kaidan, “On the ranges of some functionals on special classes of analytic functions,” Ukr. Mat. Zh.,30, No. 2, 192–200 (1978).
V. Ya. Gutlyanskii, “On the ranges of some functionals and properties of level lines on classes of one-sheeted functions,” Tr. Tomsk, Inst.,200, No. 4, 71–87 (1968).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 551–555, September–October, 1979.
Rights and permissions
About this article
Cite this article
Kaidan, V.A., Pokhilevich, V.A. Boundaries of α-convexity for subclasses of starlike functions. Ukr Math J 31, 436–439 (1979). https://doi.org/10.1007/BF01126872
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01126872