Inclusion theorems of convolution operators associated with normalized hypergeometric functions

[摘要] For the normalized Gaussian hypergeometric function zF(a, b: c: z) given by F(a, b: c: Z) = Sigma(infinity)(n=0) (a,n)(b,n)/(c,n)(l,n)z(n), vertical bar z vertical bar < 1, the author aims at finding conditions on a, b and c such that the convolution operator zF(a, b: c; z) * f (z) satisfies some inclusion results in certain class of analytic functions and in particular when f is an element of P-y(beta), where P-y(beta) = {f is an element of A : Re [e(ip) ((1 - y) f(z)/z + yf'(z) - beta)] > 0, phi is an element of R, z is an element of Delta}. A convolution result for the class Py(beta) is also given. Analogous results for the confluent hypergeometric functions are also discussed. (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-01

[关键词] convex;starlike;hypergeometric functions;integral transforms