Some Properties Of Certain Analytic Function Classes

The problems of extreme problem, containing, radii of starlikeness and convex of analytic functions are highly emphasized all the time by mathematicians from all over the world. In this paper mainly do research on the problems of some subclasses of analytic functions and give some meaningful results. These generalized the previous research results and completed these problems for further research in view of the main theory. then we consummate the study of these problems.This paper contains four chapters. The first chapter is the exordium which gives a simple introduction of the phylogeny of Analytic functions and some classes and their notations that will appear and be used in the present paper. In the second chapter, a subclass UST ^k (α,β)and UCV^k(α,β)of analytic functions with negative coefficients with respect to k-symmetric points is introduced. The necessary and sufficient conditions, distortion and covering theorems, radii of starlikeness and convex and extreme points. Two close-convex and quasi-convex C (k)(λ,α,β,γ)and (?)C^k(λ,α,β,γ),which are defined and discussed in the third chapter. It studies inclusion relationships, coefficient inequalities, integral representations and convolution conditions. The forth chapter studies classes R (α,β,γ). In the this chapter, we provide necessary and sufficient coefficient conditions, radius of starlikeness and convexity ,extreme points, and estimated deviation. The results presented here would provide extensions of those given in earlier works .