New class of k-uniformly harmonic functions defined by Al-Oboudi operator

TL;DR

This paper introduces a new class of k-uniformly harmonic functions using the Al-Oboudi operator, exploring their properties and subclasses to advance understanding in harmonic function theory.

Contribution

It defines the new classes $k$-USH and $k$-UTH of harmonic functions and investigates their extreme points, distortion bounds, and other properties.

Findings

Defined the classes $k$-USH and $k$-UTH of harmonic functions.

Analyzed extreme points and distortion bounds for these classes.

Established convolution conditions and convex combination properties.

Abstract

In this paper, we introduce the class $k$-USH $(u,v,\alpha,\lambda)$ using Al-Oboudi operator which is a subclass of $k$-uniformly harmonic functions. A subclass $k$-UTH $(u,v,\alpha,\lambda)$ of $k$-USH $(u,v,\alpha,\lambda)$ is also been defined and studied in this paper. Extreme points, distortion bounds, convolution condition and convex combination of functions belonging to the class $k$-UTH $(u,v,\alpha, \lambda)$ are also studied.