Starli̇ke and convex functi̇ons of complex order

This work is based on the study of the class of univalent functions and its subclass which plays a important role in geometrical functions theory. This thesis consists of two parts. In the first part, constructing the class S of functions which are analytic and univalent in the open unit disk , some properties of coefficients, distortion and growth theorems of this class, the class P and its some properties are given. Moreover the class of starlike and convex functions and the univalent functions defined by those functions are defined and their some properties are given. In the second part, the classes of and are defined and their coefficient inequalities, extremal functions and the radius of starlikeness and convexity are given. Keywords: Univalent functions, class of starlike and convex function, class of starlike and convex function of complex order, class of Janowski functions.