On the logarithmic coefficients of Ma-Minda type convex functions

TL;DR

This paper studies specific subclasses of Ma-Minda convex functions, providing corrected and extended inequalities for their logarithmic coefficients, enhancing understanding of their coefficient bounds.

Contribution

It introduces corrected inequalities for logarithmic coefficients of Ma-Minda convex subclasses, extending previous results and clarifying earlier inaccuracies.

Findings

Established new bounds for logarithmic coefficients.

Corrected previous erroneous inequalities.

Extended known results to broader subclasses.

Abstract

In this paper, we investigate three specific subclasses of Ma-Minda type convex functions: namely, convex functions of order $\alpha$, Janowski convex functions, and Robertson functions of normalized analytic functions defined in the open unit disk. For these classes, we establish logarithmic coefficient inequalities concerning both individual coefficient estimates and weighted series. The results presented here correct some earlier erroneous results and extend several previously known ones.