A note on a class of $p$-valent starlike functions of order beta

TL;DR

This paper provides accurate coefficient bounds for a specific class of p-valent starlike functions of order beta, correcting previous inaccuracies and establishing a reliable proof for these bounds.

Contribution

The paper corrects and completes the proof of coefficient bounds for p-valent starlike functions of order beta, previously addressed incorrectly by Aouf.

Findings

Established sharp coefficient bounds for p-valent starlike functions

Corrected the proof of bounds previously given by Aouf

Enhanced understanding of the geometric properties of these functions

Abstract

In this paper we obtain sharp coefficient bounds for certain $p$-valent starlike functions of order $\beta$, $0\le \beta<1$. Initially this problem was handled by Aouf in "M. K. Aouf, On a class of $p$-valent starlike functions of order $\alpha$, Internat. J. Math. $\&$ Math. Sci. 1987;10:733--744". We pointed out that the proof given by Aouf was incorrect and a correct proof is presented in this paper.