Some subclasses of meromorphic harmonic functions defined by using generalized differential operators

This work consists of five chapters. In the first chapter the necessary knowledge about development of the analytic and harmonic univalent functions are given. In the second chapter, some basic definitions and theorems are given which are the necessary for properly understanding of the following chapters. Moreover, univalent functions and some of subclasses are mentioned. In the third chapter, harmonic functions and the related basic concepts, definitions and theorems are given. Furthermore, some subclasses of harmonic univalent functions and subordination concept are mentioned. In the fourth chapter, new classes of meromorphic harmonic starlike functions defined by a new generalized differential operator in outside of the unit disc ?U zz ? ? ? : 1? are given. Furthermore, coefficients inequalities, distortion theorems and extreme points for the functions belonging to these classes are obtained. In the fifth chapter, new classes of multivalent meromorphic harmonic and orientation preserving functions are defined by a new generalized Al-Oboudi differential operator in outside of the unit disc ?U zz ? ? ? : 1? are given. Furthermore, coefficient bounds, distortion theorems, extreme points and convex combinations for the functions in these classes are determined. Key Words: Analytic, Harmonic univalent functions, Meromorphic functions, Al-Oboudi differential operator, Coefficient inequalities, Extreme point