Introducing a Novel Subclass of Harmonic Functions with Close-to-Convex Properties

TL;DR

This paper introduces a new subclass of close-to-convex harmonic functions, providing coefficient conditions and a distortion theorem, which could be extended to higher-order derivatives.

Contribution

The paper presents a novel subclass of harmonic functions with close-to-convex properties, including coefficient criteria and a distortion theorem, advancing the theoretical understanding of harmonic function classes.

Findings

Established a sufficient coefficient condition for the new subclass

Proved a distortion theorem for the subclass

Laid groundwork for extending to higher-order derivatives

Abstract

In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay the groundwork for extending the findings to function classes involving higher-order derivatives.