International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 62548, 6 pages
doi:10.1155/IJMMS/2006/62548

Subordination by convex functions

Rosihan M. Ali, V. Ravichandran, and N. Seenivasagan

School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia

Received 30 July 2006; Accepted 12 November 2006

Copyright © 2006 Rosihan M. Ali et al. 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

For a fixed analytic function g(z)=z+∑n=2∞gnzn defined on the open unit disk and γ<1, let Tg(γ) denote the class of all analytic functions f(z)=z+∑n=2∞anzn satisfying ∑n=2∞|angn|≤1−γ. For functions in Tg(γ), a subordination result is derived involving the convolution with a normalized convex function. Our result includes as special cases several earlier works.