Estimates for initial coefficients of certain bi-univalent functions

TL;DR

This paper derives improved bounds for the initial coefficients of certain bi-univalent functions, enhancing existing estimates by considering subclasses of univalent functions and their inverses.

Contribution

It provides new, sharper coefficient estimates for bi-univalent functions within specific subclasses, advancing the understanding of their coefficient bounds.

Findings

Improved bounds for initial coefficients of bi-univalent functions.

Enhanced estimates for functions and their inverses in specific subclasses.

Contributes to the theory of univalent and bi-univalent function coefficient bounds.

Abstract

Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent functions. The bounds obtained improve some existing known bounds.