Schwarz lemma and Schwarz-Pick lemma for solutions of the α-harmonic equation ☆

被引：0

作者：

Li, Ming ^{[1
]}

Ma, Xiu-Shuang ^{[2
]}

Wang, Li-Mei ^{[3
]}

机构：

[1] Changsha Univ Sci & Technol, Sch Math & Stat, 960 2 Sect Wanjiali RD S, Changsha 410004, Hunan, Peoples R China

[2] Hunan Univ Sci & Technol, Sch Math & Comp Sci, Xiangtan 411201, Peoples R China

[3] Univ Int Business & Econ, Sch Stat, 10 Huixin Dongjie, Beijing 100029, Peoples R China

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2025年 / 201卷

基金：

中国国家自然科学基金;

关键词：

Schwarz lemma; Schwarz-Pick lemma; Poisson integral; alpha-harmonic function;

D O I：

10.1016/j.bulsci.2025.103598

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of alpha-harmonic equation (alpha>-1) are investigated. By making use of the integral of trigonometric functions, we obtain these 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). (c) 2025 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：17

共 19 条

[1]

Abramowitzand M., 1965, Handbook of Mathematical Functions

[2]

Andrews G., 1999, Special functions

[3] The Schwarz-Pick lemma for planar harmonic mappings [J].

Chen HuaiHui .

SCIENCE CHINA-MATHEMATICS, 2011, 54 (06) :1101-1118

[4] Some properties of a class of elliptic partial differential operators [J].

Chen, Shaolin ;

Vuorinen, Matti .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 431 (02) :1124-1137

[5] THE BLOCH CONSTANT OF BOUNDED HARMONIC-MAPPINGS [J].

COLONNA, F .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1989, 38 (04) :829-840

[6]

Duren P. L., 2004, HARMONIC MAPPINGS PL

[7]

Heinz E., 1959, Pac. J. Math., V9, P101

[8]

Hethcote H. T. W., 1977, International Journal of Mathematical Education in Science and Technology, V8, P65, DOI 10.1080/0020739770080109

[9]

Kalaj D, 2024, COMPLEX ANAL OPER TH, V18, DOI 10.1007/s11785-024-01578-2

[10] ON HARMONIC FUNCTIONS AND THE SCHWARZ LEMMA [J].

Kalaj, David ;

Vuorinen, Matti .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (01) :161-165

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