Measures of Noncircularity and Fixed Points of Contractive Multifunctions

Measures of Noncircularity and Fixed Points of Contractive Multifunctions

<p/> <p>In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem o...

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Main Author: Marrero Isabel
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2010/340631
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spelling doaj-0248bbaef85b46449271576fa16d37de2020-11-25T00:36:58ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101340631Measures of Noncircularity and Fixed Points of Contractive MultifunctionsMarrero Isabel<p/> <p>In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.</p>http://www.fixedpointtheoryandapplications.com/content/2010/340631
collection DOAJ
language English
format Article
sources DOAJ
author Marrero Isabel
spellingShingle Marrero Isabel
Measures of Noncircularity and Fixed Points of Contractive Multifunctions
Fixed Point Theory and Applications
author_facet Marrero Isabel
author_sort Marrero Isabel
title Measures of Noncircularity and Fixed Points of Contractive Multifunctions
title_short Measures of Noncircularity and Fixed Points of Contractive Multifunctions
title_full Measures of Noncircularity and Fixed Points of Contractive Multifunctions
title_fullStr Measures of Noncircularity and Fixed Points of Contractive Multifunctions
title_full_unstemmed Measures of Noncircularity and Fixed Points of Contractive Multifunctions
title_sort measures of noncircularity and fixed points of contractive multifunctions
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2010-01-01
description <p/> <p>In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.</p>
url http://www.fixedpointtheoryandapplications.com/content/2010/340631
work_keys_str_mv AT marreroisabel measuresofnoncircularityandfixedpointsofcontractivemultifunctions
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