A generalization of close to convex functions

This work consists of three chapters. In the first chapter, common definitions about domain of complex variable functions are shown in shape. After basic definitions and theorems are given for analytic and univalent function theory, fundamental properties of univalent functions and their subclasses are mentioned shortly in this chapter. In the second chapter, after harmonic functions and the related basic concepts, definitions and theorems are mentioned. Some subclasses of harmonic univalent functions and the fundamental properties of its subclasses are given. The third chapter, performed in this study, is the main part of this thesis. Our aim is to show that common properties of harmonic functions defined by f=h(z)+g(z) form are satisfied by q–starlike harmonic functions as used general properties of quantum calculus. Also, q-close to convex functions are tried to be expressed with these properties. Keywords: Analytic, Harmonic functions, Harmonic univalent functions, Starlike, Univalent,