New subclass of harmonic univalent functions defined by integral operator

TL;DR

This paper introduces a new subclass of harmonic univalent functions defined via an integral operator, providing coefficient conditions that are both sufficient and necessary under certain conditions.

Contribution

It defines the subclass $SHP^{-m}(eta,eta)$ using an integral operator and establishes coefficient conditions for harmonic univalent functions within this class.

Findings

Provides sufficient coefficient conditions for the subclass

Shows these conditions are necessary for negative coefficients

Enhances understanding of harmonic univalent function subclasses

Abstract

In this paper, we introduce the subclass $SHP^{-m}(\alpha,\beta)$ using integral operator and give sufficient coefficient conditions for normalized harmonic univalent function in the subclass $SHP^{-m}(\alpha,\beta)$.These conditions are also shown to be necessary when the coefficients are negative.