New Subclasses of Analytic and Univalent Functions Involving Certain Convolution Operators

TL;DR

This paper introduces new subclasses of analytic and univalent functions in the unit disk using convolution-based operators, exploring their fundamental properties and inequalities.

Contribution

It defines novel classes of functions via convolution operators and investigates their basic geometric and analytic properties.

Findings

Established inclusion and growth properties of the new classes

Derived coefficient inequalities for the subclasses

Analyzed closure under integral transformations

Abstract

Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^\sigma\colon A\to A$ using the convolution *. Using these operators, we define and study new classes of functions in the unit disk. Moreover, we obtain some basic properties of the new classes, namely inclusion, growth, covering, distortion, closure under certain integral transformation and coefficient inequalities.