International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 439364 | https://doi.org/10.1155/S0161171203203021

J. A Kim, K. H. Shon, "Mapping properties for convolutions involving hypergeometric functions", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 439364, 9 pages, 2003. https://doi.org/10.1155/S0161171203203021

Mapping properties for convolutions involving hypergeometric functions

Received04 Mar 2002

Abstract

For μ0, we consider a linear operator Lμ:AA defined by the convolution fμf, where fμ=(1μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z)). Let φ(A,B) denote the class of normalized functions f which are analytic in the open unit disk and satisfy the condition zf/f(1+Az)/1+Bz, 1A<B1, and let Rη(β) denote the class of normalized analytic functions f for which there exits a number η(π/2,π/2) such that Re(eiη(f(z)β))>0, (β<1). The main object of this paper is to establish the connection between Rη(β) and φ(A,B) involving the operator Lμ(f). Furthermore, we treat the convolution I=0z(fμ(t)/t)dtf(z) for fRη(β).

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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