The Coefficients Of Certain Subclass Of Bi-univalent Functions

In the theory of univalent functions, the estimate of coefficients of univalent func-tions is an important part of this theory. Many special subclasses, such as starlike functions, convex functions, close-to-convex functions and so on, were presented after getting a lot of research results. In this paper, we give a study on coefficient estimates of the subclasses of bi-univalent functions by new method.Firstly, we introduce the developing trend of coefficient estimates, some basic concepts, basic theories and symbols of univalent functions.Secondly, we define four subclasses of bi-univalent functions, such as<S∑(λ,γ; φ) , HS∑(α),R∑(η,γ; φ), and B∑(μ;φ). Based on the research of Erhan Deniz about estimates on the first two coefficients, this paper presents new method by subordinate conditions and gets new coefficient estimates.Finally, based on contrasting the conclusions, we conclude this paper with a prospect.