Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1367–1369 | Cite as

On Some “Collateral” Effects in the Alpha-convex Theory

  • A. V. KazantsevEmail author
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev


Some effects in the α-convex theory of the univalent functions are discussed in the light of the uniqueness problem for the critical point of the conformal radius.

Keywords and phrases

Conformal radius hyperbolic derivative α-convex function best dominant 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. S. Miller, P. T. Mocanu, and M. O. Reade, “All α-convex functions are univalent and starlike,” Proc. Am. Math. Soc. 37, 553–554 (1973).MathSciNetzbMATHGoogle Scholar
  2. 2.
    S. S. Miller and P. T. Mocanu, “Univalent solutions of Briot-Bouquet differential equations,” J. Differ. Equat. 56, 297–309 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    S. S. Miller and P. T. Mocanu, “On some classes of first-order differential subordinations,” Mich. Math. J. 32, 185–195 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Z. Jakubowski and J. Kaminski, “On some classes of alpha-convex functions,” Anal. Numer. Theor. Approx. 27, 13–26 (1985).MathSciNetzbMATHGoogle Scholar
  5. 5.
    Z. Lewandowski, S. Miller, and E. Zlotkiewicz, “Generating functions for some classes of univalent functions,” Proc. Am. Math. Soc. 56, 111–117 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” Mich. Math. J. 28, 157–171 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. Szynal, “Some remarks on coefficients inequality for α-convex functions,” Bull. Acad. Polon. Sci., Ser. Math., Astron. Phys. 20, 917–919 (1972).MathSciNetzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

Personalised recommendations