A Study on Meromorphic Harmonic Starlike Functions by Using a New Generalized Differential Operator
F. Muge Sakar *
Department of Business Administration, Faculty of Management and Economics, Batman University, 72060 Batman, Turkey
H. Ozlem Guney
Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbakır, Turkey
*Author to whom correspondence should be addressed.
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.
Keywords: Harmonic functions, meromorphic, starlike functions