Certain Subclass of Harmonic Multivalent Functions Defined by New Linear Operator

TL;DR

This paper introduces a new subclass of meromorphic functions defined via a novel linear operator, exploring their geometric properties and establishing key results like coefficient estimates, distortion, growth, and convexity.

Contribution

It proposes a new linear operator to define a subclass of harmonic multivalent functions and investigates their geometric and analytic properties.

Findings

Coefficient estimates established

Distortion and growth theorems proved

Radius of starlikeness and convexity determined

Abstract

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results as coefficient estimates, distortion and growth theorems, radius of starlikeness, convexity and close to convexity, extreme points, convex linear combinations, neighbourhoods, and integral transforms for a new class.