On the Logarithmic Coefficients of Close to Convex Functions

TL;DR

This paper provides sharp estimates for the logarithmic coefficients of functions close to convex in the unit disk, enhancing understanding of their geometric properties and coefficient bounds.

Contribution

It introduces new sharp bounds for the logarithmic coefficients of close to convex functions, extending previous results in geometric function theory.

Findings

Sharp estimates for $oldsymbol{ ext{logarithmic coefficients}}$ $oldsymbol{oldsymbol{ ext{of close to convex functions}}}$.

Improved bounds for the first three logarithmic coefficients.

Enhanced understanding of the coefficient behavior in close to convex functions.

Abstract

For $f$ analytic and close to convex in $D=\{z: |z|< 1\}$, we give sharp estimates for the logarithmic coefficients $\gamma_{n}$ of $f$ defined by $\log \dfrac{f(z)}{z}=2\sum_{n=1}^{\infty} \gamma_{n}z^{n}$ when $n=1, 2,3$.