Applications of Extremal Theorem to a Class of p-Valent Analytic Functions

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Liangpeng Xiong, Xiaoli Liu, Applications of Extremal Theorem to a Class of p-Valent Analytic Functions, Int. J. Anal. Appl., 10 (1) (2016), 1-8.

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Liangpeng Xiong, Xiaoli Liu

Abstract

A subclass J_{p,\lambda}^{m,l}(\xi,\alpha) of p-valent analytic functions with a generalized multiplier transformation operator is introduced. We discuss the compactness as well as the extreme points of J_{p,\lambda}^{m,l}(\xi,\alpha) under the topology of uniform convergence. Finally, as one of the applications of extremal theorem, we solve the sharp distortion inequalities problem. Several related basic results and remarks about the old or new classes are also presented.

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