Landau type theorem for $\alpha$-harmonic mappings

TL;DR

This paper establishes a Landau type theorem for $\alpha$-harmonic mappings by deriving coefficient estimates and applying them to mappings on the unit disc, advancing understanding of their geometric properties.

Contribution

It introduces a Landau type theorem for $\alpha$-harmonic mappings, providing new coefficient estimates and extending classical results to this broader class.

Findings

Derived coefficient estimates for $\alpha$-harmonic mappings

Proved a Landau type theorem for these mappings on the unit disc

Enhanced understanding of the geometric behavior of $\alpha$-harmonic mappings

Abstract

In this paper, we first obtain an estimate of the coefficients for $\alpha$-harmonic mappings. By applying these coefficient estimates, we prove the Landau type theorem for $\alpha$-harmonic mappings defined on the unit disc $\ID$.