{"title":"Bounded variation of functions defined on a convex and compact set in the plane","authors":"Mireya Bracamonte, Juan Tutasi","doi":"10.1080/25765299.2023.2278247","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, the variation of functions has been defined, whose domain is a convex and compact set in the plane. Furthermore, in addition to presenting properties that satisfy this variation, the vector space formed by functions with finite variation is studied, demonstrating that it is a Banach space and its elements can be expressed as the difference of non-decreasing functions.","PeriodicalId":37239,"journal":{"name":"Arab Journal of Basic and Applied Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arab Journal of Basic and Applied Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/25765299.2023.2278247","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
Abstract In this paper, the variation of functions has been defined, whose domain is a convex and compact set in the plane. Furthermore, in addition to presenting properties that satisfy this variation, the vector space formed by functions with finite variation is studied, demonstrating that it is a Banach space and its elements can be expressed as the difference of non-decreasing functions.
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