关于一类非膨胀映射不动点的孔隙度结果

Applied Set-Valued Analysis and Optimization Pub Date : 1900-01-01 DOI:10.23952/asvao.4.2022.3.10

A. Zaslavski

{"title":"关于一类非膨胀映射不动点的孔隙度结果","authors":"A. Zaslavski","doi":"10.23952/asvao.4.2022.3.10","DOIUrl":null,"url":null,"abstract":". In one of our recent papers, we considered a complete metric space of nonexpansive mappings taking a bounded and closed subset of a complete hyperbolic space into the space so that the boundary of this subset is mapped back into the subset itself. Using the Baire category approach, we proved that most of these mappings possess a unique ﬁxed point which attracts all their iterates. In the present paper, we improve upon this result by showing that the complement of the set of mappings which have a ﬁxed point is not only of the ﬁrst Baire category, but also is σ -porous.","PeriodicalId":362333,"journal":{"name":"Applied Set-Valued Analysis and Optimization","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A porosity result regarding fixed points for a class of nonexpansive mappings\",\"authors\":\"A. Zaslavski\",\"doi\":\"10.23952/asvao.4.2022.3.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In one of our recent papers, we considered a complete metric space of nonexpansive mappings taking a bounded and closed subset of a complete hyperbolic space into the space so that the boundary of this subset is mapped back into the subset itself. Using the Baire category approach, we proved that most of these mappings possess a unique ﬁxed point which attracts all their iterates. In the present paper, we improve upon this result by showing that the complement of the set of mappings which have a ﬁxed point is not only of the ﬁrst Baire category, but also is σ -porous.\",\"PeriodicalId\":362333,\"journal\":{\"name\":\"Applied Set-Valued Analysis and Optimization\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Set-Valued Analysis and Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23952/asvao.4.2022.3.10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Set-Valued Analysis and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/asvao.4.2022.3.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

。在我们最近的一篇论文中，我们考虑了一个非扩张映射的完备度量空间，将一个完备双曲空间的有界闭子集映射到空间中，使得这个子集的边界被映射回子集本身。利用贝尔范畴的方法，我们证明了大多数映射都有一个唯一的不动点来吸引所有的迭代。在本文中，我们改进了这一结果，证明了具有不动点的映射集的补不仅属于第一Baire范畴，而且是σ -多孔的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A porosity result regarding fixed points for a class of nonexpansive mappings

. In one of our recent papers, we considered a complete metric space of nonexpansive mappings taking a bounded and closed subset of a complete hyperbolic space into the space so that the boundary of this subset is mapped back into the subset itself. Using the Baire category approach, we proved that most of these mappings possess a unique ﬁxed point which attracts all their iterates. In the present paper, we improve upon this result by showing that the complement of the set of mappings which have a ﬁxed point is not only of the ﬁrst Baire category, but also is σ -porous.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Set-Valued Analysis and Optimization

自引率

0.00%

发文量