Coefficient estimates, Landau's theorem and Lipschitz-type spaces on planar harmonic mappings

TL;DR

This paper explores properties of planar harmonic mappings, focusing on coefficient estimates, Landau's theorem, and Lipschitz-type spaces, providing new insights into their geometric and analytic behavior.

Contribution

It introduces new coefficient bounds and Landau's theorem results for locally univalent harmonic mappings, and studies Lipschitz-type spaces for these functions.

Findings

Derived new coefficient estimates for harmonic mappings

Established Landau's theorem for specific classes of harmonic mappings

Analyzed Lipschitz-type spaces in the context of harmonic functions

Abstract

In this paper, we investigate the properties of locally univalent and multivalent planar harmonic mappings. First, we discuss the coefficient estimates and Landau's Theorem for some classes of locally univalent harmonic mappings, and then we study some Lipschitz-type spaces for locally univalent and multivalent harmonic mappings.