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On the growth of nonvanishing analytic functions

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Abstract.

In this article by a new and simple method we derive new and old coefficient bounds and distortion theorems for functions G(z) analytic in the unit disk and satisfying \(\sup\limits _{|z|\le 1}(|G(z)|(1-|z|^2) ^\alpha )\leqq 1\) for some \(\alpha \geqq 0\). These results enable us to prove analogous theorems for the subclasses consisting of nonvanishing functions.

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Authors and Affiliations

  1. Chebotarev Research Institute, Kazan State University, 420008 Kazan, Russia, , , , , , RU

    F.G. Avhadiev

  2. Institut für Analysis, Technische Universität, D-38106 Braunschweig, , , , , , DE

    N. Schulte & K.-J. Wirths

Authors
  1. F.G. Avhadiev
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  2. N. Schulte
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  3. K.-J. Wirths
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Received: 24.4.1998

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Avhadiev, F., Schulte, N. & Wirths, KJ. On the growth of nonvanishing analytic functions. Arch. Math. 74, 356–364 (2000). https://doi.org/10.1007/s000130050455

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  • DOI: https://doi.org/10.1007/s000130050455

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