Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

TL;DR

This paper derives coefficient estimates for certain bi-univalent functions related to Ma-Minda classes, expanding understanding of their geometric properties and connections to existing results.

Contribution

It provides new coefficient bounds for bi-univalent Ma-Minda starlike and convex functions, including inverse function estimates and class connections.

Findings

Coefficient estimates for functions and their inverses are established.

Connections to known classes of univalent functions are demonstrated.

Several related function classes are analyzed with new bounds.

Abstract

Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.