Title: Applications of Extremal Theorem to a Class of p-Valent Analytic Functions
Author(s): Liangpeng Xiong, Xiaoli Liu
Pages: 1-8
Cite as:
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.


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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