Quasi-convolution of analytic functions with applications

TL;DR

This paper introduces a new quasi-convolution concept for analytic functions in the unit disk and explores its implications for the closure properties of certain classes of univalent functions under various integral operators.

Contribution

It presents a novel quasi-convolution method for analytic functions and analyzes its effects on the closure properties of specific function classes under integral transformations.

Findings

Closure properties of analytic function classes are preserved under new quasi-convolution.

The approach extends known results to new classes of integral operators.

Applications include univalent function theory and geometric function analysis.

Abstract

In this paper we define a new concept of quasi-convolution for analytic functions normalized by $f(0)=0$ and $f^\prime(0)=1$ in the unit disk $E=\{z\in \mathbb{C}\colon |z|<1\}$. We apply this new approach to study the closure properties of a certain class of analytic and univalent functions under some families of (known and new) integral operators.