{"title":"Estimation of the Modulus of Hölder Metric Regularity","authors":"Wending Xu","doi":"10.1134/S0016266322020071","DOIUrl":null,"url":null,"abstract":"<p> This paper mainly studies the modulus of Hölder metric regularity. The concepts of a generalized <span>\\(p\\)</span>-order Clarke-like set and generalized graphical derivative are introduced and used to estimate this modulus. The main result implies that it is bounded above by the upper limit of the inner norm of the inverse of generalized graphical derivative. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 2","pages":"138 - 143"},"PeriodicalIF":0.6000,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266322020071","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper mainly studies the modulus of Hölder metric regularity. The concepts of a generalized \(p\)-order Clarke-like set and generalized graphical derivative are introduced and used to estimate this modulus. The main result implies that it is bounded above by the upper limit of the inner norm of the inverse of generalized graphical derivative.
期刊介绍：
Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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