A class of univalent functions with real coefficients

TL;DR

This paper investigates a specific class of univalent functions with real positive coefficients, providing coefficient estimates, functional bounds, and conditions for starlikeness of order 1/2.

Contribution

It introduces the class \(\\mathcal{S}^+\) of univalent functions with real positive coefficients and derives new bounds and conditions for these functions.

Findings

Estimates of the Fekete-Szeg\

sharp bounds for initial and logarithmic coefficients

necessary and sufficient conditions for starlikeness of order 1/2

Abstract

In this paper we study class $\mathcal{S}^+$ of univalent functions $f$ such that $\frac{z}{f(z)}$ has real and positive coefficients. For such functions we give estimates of the Fekete-Szeg\H{o} functional and sharp estimates of their initial coefficients and logarithmic coefficients. Also, we present necessary and sufficient conditions for $f\in \mathcal{S}^+$ to be starlike of order $1/2$.