{"title":"\\（AP\\）-Henstock积分的乘子性质","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":"{\"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}","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}
Multiplier properties for the \(AP\)-Henstock integral
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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