arXiv subjects

Xiu-Shuang Ma

Publications and source records attributed to Xiu-Shuang Ma.

3 recordsLinked to original sources

arXiv2025

Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk

This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane, and an explicit formulation of its extension function is provided. Additionally, the quasiconformal extendibility of harmonic mappings defined in the exterior of the unit disk is explored.

math.CV↗

arXiv2023

Schwarz Lemma and Schwarz-Pick Lemma for solutions of the $α$-harmonic equation

In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of $α$-harmonic equation for $α>-1$ are investigated. By making use of the integral of trigonometric functions, we obtain the two types of inequalities in terms of hypergeometric functions which improve the corresponding results due to Khalfallah et al. (Complex Var. Elliptic Equ., 2023) and Li et al. (Bull. Malays. Math. Sci. Soc., 2022).

math.CV↗

arXiv2021

Harmonic spirallike functions and harmonic strongly starlike functions

Harmonic functions are natural generalizations of conformal mappings. In recent years, a lot of work have been done by some researchers who focus on harmonic starlike functions. In this paper, we aim to introduce two classes of harmonic univalent functions of the unit disk, called hereditarily $λ$-spirallike functions and hereditarily strongly starlike functions, which are the generalizations of $λ$-spirallike functions and strongly starlike functions, respectively. We note that a relation can be obtained between this two classes. We also investigate analytic characterization of hereditarily spirallike functions and uniform boundedness of hereditarily strongly starlike functions. Some coefficient conditions are given for hereditary strong starlikeness and hereditary spirallikeness. As a simple application, we consider a special form of harmonic functions.

math.CV↗