{"title":"Schwarz lemma and Schwarz-Pick lemma for solutions of the α-harmonic equation","authors":"Ming Li , Xiu-Shuang Ma , Li-Mei Wang","doi":"10.1016/j.bulsci.2025.103598","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of <em>α</em>-harmonic equation (<span><math><mi>α</mi><mo>></mo><mo>−</mo><mn>1</mn></math></span>) 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).</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103598"},"PeriodicalIF":1.3000,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449725000247","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of α-harmonic equation () 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).
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