Coefficient problems for certain Close-to-Convex Functions

TL;DR

This paper establishes sharp bounds on the second Hankel determinant of logarithmic coefficients for normalized analytic functions satisfying specific differential inequalities, advancing the understanding of coefficient problems in close-to-convex functions.

Contribution

It provides new sharp bounds for the second Hankel determinant of logarithmic coefficients in a class of close-to-convex functions, a novel result in geometric function theory.

Findings

Sharp bounds for the second Hankel determinant are derived.

Results apply to functions satisfying certain differential inequalities.

The bounds improve previous estimates in the literature.

Abstract

In this paper, sharp bounds are established for the second Hankel determinant of logarithmic coefficients for normalised analytic functions satisfying certain differential inequality.