Convolution of Harmonic Mappings On The Exterior Unit Disk and the Generalized Hypergeometric Functions

Abstract

A new class is introduced consisting of harmonic univalent functions on the exterior unit disk defined by convolution. This class generates several known and new subclasses of harmonic univalent functions as special cases. A necessary and sufficient convolution condition is obtained for functions to belong to the class. A corresponding general class of harmonic functions with negative coefficients is also introduced, and coefficient condition that is both necessary and sufficient is obtained for the class. Extreme points are also determined. As applications, starlikeness conditions of the Liu-Srivastava linear operator involving the generalized hypergeometric functions are discussed.