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arXiv · 2603.15659

Sharp Estimates of Logarithmic Coefficients for a Certain Class of Starlike Functions

Molla Basir Ahamed·Sanju Mandal
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Abstract

In this article, we investigate the extremal properties of logarithmic coefficients for the class $\mathcal{S}_{ch}^*$ of starlike functions associated with the hyperbolic cosine function. We establish the sharp upper bounds for the initial logarithmic coefficients $\gamma_n$ for $n=1, 2, 3$, and determine the precise bound for the second Hankel determinant $H_{2,1}(F_f/2)$ within this class. Furthermore, we extend our analysis to the inverse functions, deriving sharp estimates for the logarithmic inverse coefficients and the corresponding second Hankel determinant $|H_{2,1}(F_{f^{-1}}/2)|$. Additionally, we provide sharp bounds for the moduli differences of both logarithmic and inverse logarithmic coefficients. The sharpness of all obtained inequalities is verified through the construction of specific extremal functions.

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Molla Basir Ahamed, Sanju Mandal. 2026-03-08. Sharp Estimates of Logarithmic Coefficients for a Certain Class of Starlike Functions. https://arxiv.org/abs/2603.15659

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