Integral operator on certain subclass of analytic function with negative coefficients

TL;DR

This paper investigates a specific subclass of analytic functions with negative coefficients defined via an integral operator in the unit disk, providing coefficient estimates, closure, distortion theorems, and studying uniformly convex and starlike functions.

Contribution

It introduces a new subclass of analytic functions with negative coefficients defined by an integral operator and explores their properties and special subclasses.

Findings

Coefficient estimates derived for the subclass

Closure and distortion theorems established

Detailed analysis of uniformly convex and starlike functions

Abstract

In this paper, we study subclass of analytic function with negative coefficient defined by integral operator in the unit disc $U = \left\{ {z \in C:\left| z \right| < 1} \right\}$. The results are included coefficient estimates, closure theorem and distortion theorems of functions belonging to this subclass. Also, we presented detailed study of uniformly convex and uniformly starlike functions.