The Problem Of Coefficients Of Univalent Functions

In this thesis, we investigate the Fekete-Szego problem for two subclasses of Bazilevic functions and the subclass of starlike functions with negative coefficients which is defined by the salagean operator ,at the same time ,using the D^λ operator we introduced a new subclass B_λ (μ,α,A,B), the related properties are discussed.In chapter 1,we study the Fekete-Szego problem for two subclasses of univalent functions.In subchapter 1.1 we investigate the Fekete-Szego problem for the subclassB(α.β.γ). The sharp results are obtained, which generalize the relative results of some authors. In subchapter 1.2, the Fekete-Szego problem for the subclass B_γ(α,β) are studied . We obtain the sharp estimates of |α₃ -μα₂²| which improvethe results of [1].In chapter 2 using the salagean operator, we introduce the subclass T_n{m,λ,μ,α) with negative coefficients, some results such as coefficients estimates,distortion theorems for this class are given here, which generalize some results obtained by Altintas, Muhammet Kamali, Srivastava et al, Chatterjea and so on.In chapter 3 we introduce a new subclass B_λ(μ,α,A,B),the subordinationrelations and the inquality properties are discussed by using differential subordinationmethod.The results obtained generalize results of some previous authors.