A Study on Meromorphic Harmonic Starlike Functions by Using a New Generalized Differential Operator

Abstract

In this study, a new generalized differential operator D was obtained first.Then this new differential operator was used to introduce a new class GS(n) of univalent meromorphic harmonic starlike functions exterior to the unit disc eU := {z |z| > 1}. Especially, coefficient bounds for this class have been examined. This coefficient condition is also necessary for the class GS(n) which is subclass of meromorphic harmonic functions. Furthermore, some other properties such as distortion theorems and extreme points for these classes were obtained and relevant results were given.