Some properties of a Subclass of Univalent Functions

TL;DR

This paper investigates a specific subclass of univalent functions in the unit disk, providing coefficient bounds and distortion theorems using the Salagean differential operator, thus generalizing existing results.

Contribution

It introduces new bounds and theorems for a subclass of univalent functions defined via the Salagean operator, unifying several known results.

Findings

Coefficient bounds for the subclass

Distortion theorems established

Generalization of known univalent function results

Abstract

We give some coefficient bounds and distortion theorems for a subclass of univalent functions in the unit disk, and defined using the S\^{a}l\^{a}gean differential operator. The results generalize and unify some well known results for several subclasses of univalent functions defined on the unit disk having form $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$, normalized such that $f(0)=0$ and $f^\prime(0)=1$.