Journal of Mathematical Sciences

, Volume 207, Issue 6, pp 832–838 | Cite as

Inequalities for the Moduli of Circumferentially mean p-Valent Functions

  • V. N. Dubinin

Let f be a circumferentially mean p-valent function in the disk |z| < 1 with Montel’s normalization f(0) = 0, f(ω) = ω (0 < ω < 1). Under an additional assumption on the covering of concentric circles by f, sharp lower and upper bounds on the modulus |f(z)| for some z ∈ (−1, 0) are established. It is shown that for nontrivial bounds to hold, such an assumption is necessary. Bibliography: 15 titles.


Riemann Surface Branch Point Univalent Function Conformal Mapping Jordan Curve 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Far Eastern Federal UniversityVladivostokRussia

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