The logarithmic derivative of areally mean p-valent functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:296

Article

Dong, XH

关键词: areally mean p-valent function;    logarithmic derivative;    asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2004.04.032

来源: Elsevier

【 摘 要 】

Let U(p, k) denote the class of functions f which are areally mean p-valent and have k maximal growth directions in Delta = {z: \z\ < 1}. In this paper we give an asymptotic formula of the mean square of the logarithmic derivative f'/f for f is an element of U(p, k) with some restricted condition. This generalizes the corresponding result in [J. Anal. Math. 36 (1979) 36-43]. Also we construct a function f c U(p, k) which does not satisfy this asymptotic formula. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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