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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 27, Pages 1751-1754
http://dx.doi.org/10.1155/S0161171203204087

An application of a subordination chain

Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148, Punjab 106, India

Received 12 April 2002

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.

Abstract

Let K denote the class of functions g(z)=z+a2z2+ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for gK, f(z)+αzf(z)g(z)+αzg(z) in E implies that f(z)g(z) in E, where α>0 is a real number and the symbol “” stands for subordination.