New Hohlov Type Integral Operator involving Clausen's Hypergeometric Functions

TL;DR

This paper introduces a new integral operator involving Clausen's Hypergeometric Functions, analyzing its properties and effects on univalent functions using convolution techniques.

Contribution

It defines a novel Hohlov type integral operator with Clausen's Hypergeometric functions and explores its geometric properties for various subclasses of univalent functions.

Findings

Conditions on parameters for the operator are established.

The operator's impact on univalent function subclasses is analyzed.

Geometric properties of Clausen's Hypergeometric functions are studied.

Abstract

We consider the integral operator $\mathcal{I}^{a,b,c}_{d,e}(f)(z)$ involving Clausen's Hypergeometric Function by means of convolution introduced by Chandrasekran and Prabhakaran for investigation. The conditions on the parameters $ a,b, c$ are determined using the integral operator $\mathcal{I}^{a,\frac{b}{2},\frac{b+1}{2}}_{\frac{c}{2}, \frac{c+1}{2}}(f)(z)$ to study the geometric properties of Clausen's Hypergeometric Function for various subclasses of univalent functions.