The Problem Of Coefficients Of Univalent Function

Content: In this thesis , we investigate the problem of adjacent coefficients of univalent function and the Fekete-Szego problem .In chapter 1 , we study the relative growth of adjacent coefficients of univalentfunction .For the function, and when f isa -spiral-like function, we obtain the exact estimate for the order of .In chapter 2 , we investigate the asymptotic characteristic of thedifference of the moduli of adjacent coefficients of univalent function. Let f be a univalent function with maximal growth on a direction.. For the function f(z) L, the asymptoticcharacteristic of adjacent coefficients studied. In chapter 3 , we investigate the Fekete-Szego problem for two new class D(λ,α,δ,β) and S*(β) of analytic functions. Two new class D(λ,α,δ,β) and S*(β) of analytic functions are introduced, we discuss the Fekete-Szego inequality for D(λ,α,δ,β) and S*(β). On some conditions , the sharp results are obtained, which generalizes the related results of some authors.