Lakmon Kodjovi, S. Kenny, Ayassou Emmanuel, Tchariè Kokou
{"title":"On the Riesz Integral Representation of Additives Set-Valued Maps (I)","authors":"Lakmon Kodjovi, S. Kenny, Ayassou Emmanuel, Tchariè Kokou","doi":"10.9734/BJAST/2017/30901","DOIUrl":null,"url":null,"abstract":"In this paper we generalize the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space. We deduce the Riesz integral representation results for set-valued maps, for vector-valued maps of Diestel-Uhl and for scalar-valued maps of Dunford-Schwartz.","PeriodicalId":91221,"journal":{"name":"British journal of applied science & technology","volume":" ","pages":"1-7"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"British journal of applied science & technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.9734/BJAST/2017/30901","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we generalize the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space. We deduce the Riesz integral representation results for set-valued maps, for vector-valued maps of Diestel-Uhl and for scalar-valued maps of Dunford-Schwartz.