Certain subclass of harmonic functions associated with univalent functions

TL;DR

This paper introduces a new subclass of sense-preserving harmonic functions linked to analytic functions satisfying a differential inequality, exploring their properties and conditions for inclusion of specific functions.

Contribution

It defines a novel subclass of harmonic functions associated with differential inequalities and investigates their fundamental properties and inclusion criteria.

Findings

Established radius properties and convolution results.

Derived coefficient and growth estimates.

Provided conditions for harmonic univalent polynomials to belong to the subclass.

Abstract

In this paper, we define a subclass of sense-preserving harmonic functions associated with a class of analytic functions satisfying a differential inequality. We then establish a close relation between both subclasses. Further, we obtain some characteristic properties, including radius properties, convolution, coefficient estimates and their properties, growth estimates, and convex combination for the functions in the defined subclass. At last, we produce conditions for some special functions as well as harmonic univalent polynomials to belong to the defined subclass of harmonic functions.