• GOODMAN-RØNNING TYPE CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING CONVOLUTIONAL OPERATORS

Abstract

In this paper, we study a convolutional approach of harmonic univalent functions. For this purpose we introduce a Goodman-Rønning type class of harmonic univalent functions involving convolutional operators. A sufficient coefficient condition for the normalized harmonic functions to be in this class is obtained. It is also shown that this coefficient condition is necessary for the functions in its subclass . We further obtain extreme points, bounds and a covering result for the class and show that this class is closed under convolutions and convex combinations. Conditions on the coefficients of and lead various well-known results proved earlier as well as to generate number of new results.