The Properties Of Several Classes Of Complex Functions

Content: In this thesis, we investigate two classes of analytic functions and certain kind of harmonic univalent function with negative coefficients. We drive some properties of these classes of functions. The whole thesis includes three chapters. In the first chapter: the author introduces a new class of analytic function C(λ,β,A,B) which is the generalization of the class of analytic function C(λ,β) and through subordination of the function we drive the distortion theorems,coefficient estimate, convolution properties etc for the class C(λ,β,A,B). In the second chapter: The author introduces certain class of analytic function K(λ,β) defined in the open unit disc. It is the generalization of the function K(β)--the-close-to convex function of kind β .We study its Fekete - Szeg(o|¨) problem through the comparison among the coefficients ,obtain its Fekete - Szeg(o|¨) inequality and prove the result is sharp in some conditions. In the last chapter: the author investigates certain kind of harmonic univalent function with negative coefficients and obtain some sufficient-necessary conditions for this new kind function. In this paper, we obtain many new results some of which are the generalization of other papers.