On Some Classes Of Analytic Functions

Content: In this thesis, we investigate properties and coefficients maximum problem of some analytic functions in function theory, the research center is univalent function. We not only propel some results but also obtain some new results.In chapter 2, we investigate the maximum problem |a₃ - μa₂²| of functional H_c(β), which is Fekete-Szego problem. When f(z)∈H_c(β), we obtain the sharp bounds of |a₃ - μa₂²|.In chapter 3, we introduce a new family of functions with negative coefficients T(λ), 0≤λ≤1. We study coefficients estimate, distortion and covering theorems, radius of convexity and some other facts for the class T(λ).In chapter 4, we discuss some characteristics of the extended close-to-convexfunction family, including: the exact values of the n th coefficient; if f(z)∈C', we proved F(z) = . We also discussed the coefficient estimate of the extended close-to-convex function family with negative coefficients (C')₀.In chapter 5, on the base of α -spiral-like functions'definition, we introduce and study a class of analytic function S_α (λ,β) defined by D^λ operator. We deduce the integral expression of functions in S_α(λ,β). Study some integral operation and hadamard theorems of functions in S_α (λ,β).