الفهرس 
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Abstract
The purpose of this thesis is to define and study properties for classes of univalent functions defined in the open unit disc and in the punctured unit disc in the complex plane. These classes are defined by using some q⎼difference operators. Furthermore, we study classes of complex order associated with quasi-subordination, bi⎼univalent functions and Chebyshev polynomials and obtained coefficient bounds and Fekete-Szego inequalities for functions in them. Also, we study the classes of analytic functions associated with varying arguments of coefficients and obtained various properties for functions in them. Further, we define classes of uniformly starlike and convex functions associated with generalized q⎼Salagean and q⎼difference operators and we obtain some properties for functions in these classes. Finally, we study some classes of meromorphic univalent functions related to different difference operators. This thesis consists of six chapters: Chapter 1. This chapter is considered as an introductory chapter and contains basic concepts, definitions and preliminary results which are essential for completing the results and techniques used in subsequent chapters. Chapter 2. We define and study the classes of complex order related to the principal of subordination and quasi subordination and we obtain coefficient bounds and Fekete-Szego inequalities for functions belonging to these classes. Chapter 3. By using the principal of subordination and Chebyshev polynomials we define and study classes of bi⎼univalent functions and obtain coefficient bounds and Fekete-Szego inequalities for these classes. Chapter 4. We defined classes with varying arguments of coefficients, and study coefficient estimates, distortion theorems and extreme points for functions in these classes. Chapter 5. We define and study classes of uniformly starlike (convex) functions, and obtained some analytical and geometric properties such as coefficient estimates, growth and distortion theorems, closure theorems, radii of starlikeness, convexity and close-to-convexity, also we determine partial sums for functions in these classes. Chapter 6. We define a new operator and some classes of meromorphic univalent functions, and study coefficient estimates, growth and distortion theorems, closure theorems, radii of starlikeness, convexity and close-to-convexity, modified Hadamard product and family of integral operators for functions in these classes.