On certain properties of some subclasses of univalent functions

TL;DR

This paper investigates specific properties of subclasses of univalent functions, identifying disks where a particular real part condition holds, contributing to the understanding of their geometric behavior.

Contribution

It determines the radii within which certain real part inequalities are satisfied for various classes of univalent functions.

Findings

Identified disks where the real part condition holds for different subclasses.

Provided bounds on the radii for the property to be valid.

Enhanced understanding of the geometric properties of univalent functions.

Abstract

In this paper we determine the disks $|z|<r\le1$ where for different classes of univalent functions, we have the property $${\rm Re}\left\{2\frac{zf'(z)}{f(z)}-\frac{z f''(z)}{f'(z)}\right\}>0\qquad (|z|<r).$$