{"title":"Multiplier properties for the \\(AP\\)-Henstock integral","authors":"Kwancheol Shin, Ju Han Changwon Yoon","doi":"10.30538/psrp-oma2022.0103","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate some properties of the \\(AP\\)-Henstock integral on a compact set and prove that the product of an \\(AP\\)-Henstock integrable function and a function of bounded variation is \\(AP\\)-Henstock integrable. Furthermore, we prove that the product of an \\(AP\\)-Henstock integrable function and a regulated function is also \\(AP\\)-Henstock integrable. We also define the \\(AP\\)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30538/psrp-oma2022.0103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we investigate some properties of the \(AP\)-Henstock integral on a compact set and prove that the product of an \(AP\)-Henstock integrable function and a function of bounded variation is \(AP\)-Henstock integrable. Furthermore, we prove that the product of an \(AP\)-Henstock integrable function and a regulated function is also \(AP\)-Henstock integrable. We also define the \(AP\)-Henstock integral on an unbounded interval, investigate some properties, and show similar multiplier properties.
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