Sharp Estimate of Fifth Coefficient for Ma Minda Starlike and Convex Functions

TL;DR

This paper derives a precise upper bound for the fifth coefficient of certain normalized analytic functions related to Ma Minda subclasses, generalizing known results for various starlike function classes.

Contribution

It provides a sharp estimate for the fifth coefficient of functions subordinate to a Ma Minda type function, extending existing bounds for subclasses of starlike functions.

Findings

Sharp bound for the fifth coefficient of Ma Minda starlike functions

Generalizes known coefficient estimates for various subclasses

Applicable to functions satisfying specific subordination conditions

Abstract

\noindent In the present investigation, we find the sharp bound of fifth coefficient of analytic normalized function $f$ satisfying $z f'(z)/f(z) \prec \varphi(z)$ when coefficients of $\varphi$ satisfy certain conditions. For an appropriate choice of $\varphi$, the already known estimates for various other subclasses of starlike functions follow directly from the obtained result.