Convolution Properties of Classes of Analytic and Meromorphic Functions. (13th June 2010) - Ali, Rosihan M.; Mahnaz, Moradi Nargesi; Ravichandran, V.; Subramanian, K. G.
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.