Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 385728, 14 pages
doi:10.1155/2010/385728
Research Article

Convolution Properties of Classes of Analytic and Meromorphic Functions

Rosihan M. Ali,1 Moradi Nargesi Mahnaz,1 V. Ravichandran,2 and K. G. Subramanian1

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia
2Department of Mathematics, University of Delhi, Delhi 110 007, India

Received 30 October 2009; Accepted 13 May 2010

Academic Editor: Sin E. Takahasi

Copyright © 2010 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

General classes of analytic functions defined by convolution with a fixed analytic function are introduced. Convolution properties of these classes which include the classical classes of starlike, convex, close-to-convex, and quasiconvex analytic functions are investigated. These classes are shown to be closed under convolution with prestarlike functions and the Bernardi-Libera integral operator. Similar results are also obtained for the classes consisting of meromorphic functions in the punctured unit disk.