{"title":"A note on collectively coincidence theory for lower semicontinuous maps","authors":"Donal O’Regan","doi":"10.1016/j.nonrwa.2024.104272","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we present collectively fixed point theory for lower semicontinuous maps. In addition we present coincidence results between <span><math><mrow><mi>K</mi><mi>K</mi><mi>M</mi></mrow></math></span> type maps and lower semicontinuous maps. Our arguments are based on the Schauder-Tychonoff fixed point theorem and a fixed point result based on <span><math><mrow><mi>K</mi><mi>K</mi><mi>M</mi></mrow></math></span> self maps on an admissible convex set in a Hausdorff topological vector space. As an application we present a new (Nash) equilibrium result for economies.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104272"},"PeriodicalIF":1.8000,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824002116","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper we present collectively fixed point theory for lower semicontinuous maps. In addition we present coincidence results between type maps and lower semicontinuous maps. Our arguments are based on the Schauder-Tychonoff fixed point theorem and a fixed point result based on self maps on an admissible convex set in a Hausdorff topological vector space. As an application we present a new (Nash) equilibrium result for economies.
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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