Several properties of $\alpha$-harmonic functions in the unit disk

TL;DR

This paper investigates properties of alpha-harmonic functions in the unit disk, deriving inequalities, coefficient estimates, and a Landau type theorem to deepen understanding of their behavior.

Contribution

It introduces a Schwarz-Pick type inequality and coefficient estimates for alpha-harmonic functions, along with a Landau type theorem, advancing the theoretical framework for these functions.

Findings

Established a Schwarz-Pick type inequality for alpha-harmonic functions.

Derived coefficient estimates for alpha-harmonic functions.

Proved a Landau type theorem for alpha-harmonic functions.

Abstract

The aim of this paper is to obtain the Schwarz-Pick type inequality for $\alpha$-harmonic functions $f$ in the unit disk and get estimates on the coefficients of $f$. As an application, a Landau type theorem of $\alpha$-harmonic functions is established.