On hypergeometric functions and function spaces

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:139

Article

Balasubramanian, R ; Ponnusamy, S ; Vuorinen, M

关键词: univalent;    starlike;    convex;    close-to-convex;    hypergeometric functions;   

DOI  :  10.1016/S0377-0427(01)00417-4

来源: Elsevier

【 摘 要 】

The aim of this paper is to discuss the role of hypergeometric functions in function spaces and to prove some new results for these functions. The first part of this paper proves results such as monotone, convexity and concavity properties of sums of products of hypergeometric functions. The second part of our results deals with the space A of all normalized analytic functions f, f(0) = 0 = f'(0) - 1, in the unit disk Delta and the subspace R(beta) = {f is an element of A: There Exists eta is an element of R such that Re e(ieta)(f'(z) - beta) > 0, z is an element of Delta}. for f is an element of A, we consider integral transforms of the type Vlambda(f) = integral(0)(1) lambda(t)(f(tz))/(t) dt, where lambda(t) is a real valued nonnegative weight function normalized so that integral(0)(1) lambda(t) = 1. We obtain conditions on beta and the function lambda such that V-lambda(f) takes each member of R(beta) into a starlike function of order beta, beta is an element of [0, 1/2]. These results extend and improve the earlier known results in these directions. We end the paper with an open problem. (C) 2002 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free