Coefficient Estimates for Certain Classes of Bi-Univalent Functions

Abstract EN

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.