Some classes involving analytic functions

This thesis consists of six chapters. In Chapter 1, a detailed literature review and motivation of the thesis are presented. In Chapter 2, related concepts and definitions of some functions to be used in the thesis are given. Also, the basic well-known results are presented and some theorems and lemmas required to derivate the results in the thesis are recalled. In Chapter 3, a group of analytic univalent functions in the unit disk is examined. This class is defined by a differential operator involving Chebyshev polynomials. In Chapter 4, a class of univalent functions with negative coefficients are introduced by defining a new operator, and various properties, like, arithmetic mean, univalent starlike function, univalent convex function, univalent close-to-convex function, and convolution operator are obtained. In addition, inclusive properties of the class are investigated, and some results are obtained by applying integral operators. In Chapter 5, a new subclass of meromorphic univalent functions with positive coefficients defined by Ruscheweyh is studied. Moreover, their several geometric properties, like, coefficient estimates and distortion bounds are discussed. In Chapter 6, information about the obtained results and the future work that is planned are explained.