Univalency of weighted integral transforms of certain functions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:193

Article

Barnard, R. W. ; Naik, S. ; Ponnusamy, S.

关键词: subordination;    Gaussian hypergeometric function;    univalent function;    starlike function;    convex function;    Hadamard product;   

DOI  :  10.1016/j.cam.2005.06.025

来源: Elsevier

【 摘 要 】

For beta < 1 and gamma >= 0, let P gamma(beta) denote the class of all normalized analytic functions f in the unit disc such that [GRAPHICS] for some eta epsilon R. For f epsilon P-gamma(beta) we consider the integral transform [GRAPHICS] where lambda(t) is a real-valued nonnegative weight function so that integral(1)(0)lambda(t) dt = 1. The main aim of this paper is to find conditions such that V-lambda(f) epsilon P-1 (alpha) whenever f epsilon P-gamma(beta) for gamma >= 1. We also obtain conditions such that V-lambda(f) epsilon P-1 (beta') whenever f epsilon P-0(beta) for various choices of lambda(t). As a useful consequence, we find conditions for certain hypergeometric functions to be univalent. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free