New subclasses of bi-univalent functions

A function analytic in the open unit disk is said to be bi-univalent in if both the function and its inverse map are univalent there. The bi-univalency condition imposed on the functions analytic in makes the behavior of their coefficients unpredictable. Not much is known about the behavior of the higher order coefficients of classes of bi-univalent functions. We use Faber polynomial expansions of bi-univalent functions to obtain estimates for their general coefficients subject to certain gap series as well as providing bounds for early coefficients of such functions.

https://downloads.hindawi.com/journals/ijmms/2013/190560.pdf

Coefficient Estimates for Certain Classes of Bi-Univalent Functions

On a new subclass of bi-univalent functions

On certain subclasses of multivalent functions associated with an extended fractional differintegral operator

In this paper, we obtain initial coefficient bounds for functions belong to a subclass of analytic bi-univalent functions related to pseudo-starlike functions by using the Chebyshev polynomials and also we find Fekete-Szego inequalities for this class.

Gejun Bao

Papers

Some Properties of a Class of Analytic Functions