Existence of fixed points on compact epilipschitz sets without invariance conditions

Existence of fixed points on compact epilipschitz sets without invariance conditions

We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set). Equivalently this provides existence of fixed points of the map x↦x−f(x)....

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Main Authors: Marc Quincampoix, Mikhail Kamenskii
Format: Article
Language:English
Published: SpringerOpen 2005-10-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/FPTA.2005.267
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spelling doaj-80724c1fe0ec43f9a895fbec166265ef2020-11-25T00:04:47ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122005-10-012005326727910.1155/FPTA.2005.267Existence of fixed points on compact epilipschitz sets without invariance conditionsMarc QuincampoixMikhail KamenskiiWe provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set). Equivalently this provides existence of fixed points of the map x↦x−f(x). The main point of our result lies in the fact that we do not impose that f(x) is an “inward vector†for all point x of the boundary of K. Some extensions of the existence of equilibria result are also discussed for continuous functions and set-valued maps.http://dx.doi.org/10.1155/FPTA.2005.267
collection DOAJ
language English
format Article
sources DOAJ
author Marc Quincampoix
Mikhail Kamenskii
spellingShingle Marc Quincampoix
Mikhail Kamenskii
Existence of fixed points on compact epilipschitz sets without invariance conditions
Fixed Point Theory and Applications
author_facet Marc Quincampoix
Mikhail Kamenskii
author_sort Marc Quincampoix
title Existence of fixed points on compact epilipschitz sets without invariance conditions
title_short Existence of fixed points on compact epilipschitz sets without invariance conditions
title_full Existence of fixed points on compact epilipschitz sets without invariance conditions
title_fullStr Existence of fixed points on compact epilipschitz sets without invariance conditions
title_full_unstemmed Existence of fixed points on compact epilipschitz sets without invariance conditions
title_sort existence of fixed points on compact epilipschitz sets without invariance conditions
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2005-10-01
description We provide a new result of existence of equilibria of a single-valued Lipschitz function f on a compact set K of â„Ân which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set). Equivalently this provides existence of fixed points of the map x↦x−f(x). The main point of our result lies in the fact that we do not impose that f(x) is an “inward vector†for all point x of the boundary of K. Some extensions of the existence of equilibria result are also discussed for continuous functions and set-valued maps.
url http://dx.doi.org/10.1155/FPTA.2005.267
work_keys_str_mv AT marcquincampoix existenceoffixedpointsoncompactepilipschitzsetswithoutinvarianceconditions
AT mikhailkamenskii existenceoffixedpointsoncompactepilipschitzsetswithoutinvarianceconditions
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