$$\mathbb {P}$$ 集上的变分原理、定点和耦合定点

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-31 DOI:10.1007/s11784-024-01123-w

Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov

{"title":"$$\\mathbb {P}$$ 集上的变分原理、定点和耦合定点","authors":"Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov","doi":"10.1007/s11784-024-01123-w","DOIUrl":null,"url":null,"abstract":"We prove a generalization of Ekeland’s variational principal using the notion of \$\\mathbb {P}\$ sets. Using this result, we give proofs for fixed point theorems on partially ordered sets. Furthermore, one can obtain theorems for coupled fixed points using this technique. We demonstrate the procedure for proving such theorems.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A variational principle, fixed points and coupled fixed points on $$\\\\mathbb {P}$$ sets\",\"authors\":\"Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov\",\"doi\":\"10.1007/s11784-024-01123-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a generalization of Ekeland’s variational principal using the notion of \\\$\\\\mathbb {P}\\\$ sets. Using this result, we give proofs for fixed point theorems on partially ordered sets. Furthermore, one can obtain theorems for coupled fixed points using this technique. We demonstrate the procedure for proving such theorems.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11784-024-01123-w\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11784-024-01123-w","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

我们用 $\mathbb {P}$ 集的概念证明了埃克兰德变分本原的广义。利用这一结果，我们给出了部分有序集合上的定点定理的证明。此外，我们还可以利用这一技术得到耦合定点定理。我们演示了证明此类定理的过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$A variational principle, fixed points and coupled fixed points on $$\mathbb {P}$$ sets$

查看原文本刊更多论文

A variational principle, fixed points and coupled fixed points on $$\mathbb {P}$$ sets

We prove a generalization of Ekeland’s variational principal using the notion of $\mathbb {P}$ sets. Using this result, we give proofs for fixed point theorems on partially ordered sets. Furthermore, one can obtain theorems for coupled fixed points using this technique. We demonstrate the procedure for proving such theorems.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.