{"title":"抽象凸空间上multimaps的最佳逼近","authors":"Sehie Park","doi":"10.22771/NFAA.2021.26.01.12","DOIUrl":null,"url":null,"abstract":"In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumban, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrovic-Hussain-Sen-Radenovic on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"BEST APPROXIMATIONS FOR MULTIMAPS ON ABSTRACT CONVEX SPACES\",\"authors\":\"Sehie Park\",\"doi\":\"10.22771/NFAA.2021.26.01.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumban, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrovic-Hussain-Sen-Radenovic on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.\",\"PeriodicalId\":37534,\"journal\":{\"name\":\"Nonlinear Functional Analysis and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Functional Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22771/NFAA.2021.26.01.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Functional Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22771/NFAA.2021.26.01.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
BEST APPROXIMATIONS FOR MULTIMAPS ON ABSTRACT CONVEX SPACES
In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumban, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrovic-Hussain-Sen-Radenovic on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.
期刊介绍:
The international mathematical journal NFAA will publish carefully selected original research papers on nonlinear functional analysis and applications, that is, ordinary differential equations, all kinds of partial differential equations, functional differential equations, integrodifferential equations, control theory, approximation theory, optimal control, optimization theory, numerical analysis, variational inequality, asymptotic behavior, fixed point theory, dynamic systems and complementarity problems. Papers for publication will be communicated and recommended by the members of the Editorial Board.