On some properties of logarithmic coefficients of inverse of univalent functions

TL;DR

This paper investigates properties of initial logarithmic coefficients of inverse univalent functions, providing estimates and sharp bounds, especially for convex functions.

Contribution

It offers new estimates and bounds for the initial logarithmic coefficients of inverse univalent functions, including the convex case.

Findings

Sharp bounds for the modulus of initial coefficients

Estimates for the difference of consecutive coefficients

Special treatment of convex functions

Abstract

In this paper we consider some properties of the initial logarithmic coefficients for inverse functions of functions univalent in the unit disc. The case of convex functions is treated separately. We give estimate, in some cases sharp, of the modulus of the initial coefficients, as well as the difference of the modulus of two consecutive coefficients.