NEW CLASSES OF HARMONIC FUNCTIONS DEFINED BY FRACTIONAL OPERATOR

F.MUGE SAKAR1, YASEMIN BAGCI2, H. }OZLEM GUNEY

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Abstract

In the present study, we introduce an investigation of new subclasses of harmonic functions which are dened by fractional operator. Firstly, using by fractional operator, we dene new subclasses of harmonic functions. Later, we obtain main theorems of our study which contain sucient and necessary coecient bounds for functions related to the classes newly dened. Also, several particular characterization properties of these classes are given. Some of these properties involve extreme points, convex combination, distortion bounds. Finally, several corollaries of the main theorems are presented.

Keywords

Harmonic functions, fractional operator, coecient estimates, univalent.