Estimate For The Initial Coefficients Of Bi-univalent Functions

In this paper, we mainly investigate the estimate for the initial coefficients when bi-univalent functions belong to some subclasses of univalent functions. By using the method different from other authors,we get more accurate estimation.This paper mainly consists of two parts:The first part is the introduction and preliminary knowledge. The introduction introduces the history on the theory of complex function and the basis and significance to write this paper. The preliminary knowledge introduces some theoretical basis that are mentioned in this paper.The second part is the coefficient estimates. Estimates for the initial coefficients of bi-univalent functions f are investigated when f and f-1 respectively belong to some subclasses of univalent functions. Rosihan M.Ali and Kedzierawski use the analytic function with positive real part to estimate the initial coefficients when bi-univalent functions f and f-1 respectively belong to some subclasses of univalent functions. In this paper use different method to solve the above problem and make the results more accurate.The third part is the summaries of this paper and expectations in the future.