Bounds on the coefficients of certain analytic and univalent functions

TL;DR

This paper establishes optimal upper bounds on the coefficients of a specific class of analytic and univalent functions, using advanced techniques involving integral iteration and classical function theory.

Contribution

It introduces new bounds for the coefficients of the class T_n^α(β), extending previous results with a novel application of integral iteration methods.

Findings

Derived best-possible upper bounds for coefficients

Applied Nehari and Netanyahu's technique effectively

Extended understanding of coefficient bounds in univalent function classes

Abstract

For the real number $\alpha>1$, we use a technique due to Nehari and Netanyahu and an application of certain integral iteration of Caratheodory functions to find the best-possible upper bounds on the coefficients of functions of the class $T_n^\alpha (\beta)$ introduced in \cite{TOO} by Opoola.