Properties And Coefficient Estimates For Several Classes Of Bi-univalent Functions

In this thesis, we further investigate the bounds of coefficients of bi-univalent functions which have been studied by Rosihan et al. Moreover, we evaluate the initial and second coefficients of bi-univalent functions. Our results generalize some previous works. Furthermore, the conditions of starlike functions of m order and U(λ) are studied. This paper mainly consists of the following parts:In the first part, some basic concepts and symbols of classes of analytic functions are introduced for preparation. The main theories quoted by this article are provided.In the second part, several classes of bi-univalent functions are defined, and the bounds of initial coefficients for these subclasses of bi-univalent functions are investigated. The results presented in this article are more accurate than the previous results.In the third part, we define bi-univalent functions and study their properties.In the fourth part, we give the summaries of this paper and expectations in the future.