Fixed point problems: an introduction
Autor(a) principal: | |
---|---|
Data de Publicação: | 1996 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://proa.ua.pt/index.php/revdeti/article/view/19815 |
Resumo: | This paper surveys a number of fundamental results on the existence and uniqueness of fixed points for certain classes of possibly nonlinear operators. I do not try to be exhaustive, but merely to present the results that are more useful in the context of signal and image reconstruction. Some specific aspects pertaining to linear operators, and linear operators in finite dimensional spaces, are also discussed. It is shown that the set of fixed points of a nonexpansive operator is either empty or convex. Under rather general conditions this shows that the minimum norm solution of an operator equation of the form x = Ax exists and is unique, provided that is nonexpansive. This is a new result, which has interesting practical consequences in signal and image reconstruction problems and in other engineering applications. |
id |
RCAP_db210b02231818a5af7becb12716c8f0 |
---|---|
oai_identifier_str |
oai:proa.ua.pt:article/19815 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Fixed point problems: an introductionThis paper surveys a number of fundamental results on the existence and uniqueness of fixed points for certain classes of possibly nonlinear operators. I do not try to be exhaustive, but merely to present the results that are more useful in the context of signal and image reconstruction. Some specific aspects pertaining to linear operators, and linear operators in finite dimensional spaces, are also discussed. It is shown that the set of fixed points of a nonexpansive operator is either empty or convex. Under rather general conditions this shows that the minimum norm solution of an operator equation of the form x = Ax exists and is unique, provided that is nonexpansive. This is a new result, which has interesting practical consequences in signal and image reconstruction problems and in other engineering applications.UA Editora1996-01-01T00:00:00Zjournal articleinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://proa.ua.pt/index.php/revdeti/article/view/19815oai:proa.ua.pt:article/19815Eletrónica e Telecomunicações; Vol 1 No 6 (1996); 505-514Eletrónica e Telecomunicações; vol. 1 n.º 6 (1996); 505-5142182-97721645-0493reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAPenghttps://proa.ua.pt/index.php/revdeti/article/view/19815https://proa.ua.pt/index.php/revdeti/article/view/19815/14379https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessFerreira, Paulo J. S. G.2022-09-26T11:00:45Zoai:proa.ua.pt:article/19815Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:08:51.858429Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Fixed point problems: an introduction |
title |
Fixed point problems: an introduction |
spellingShingle |
Fixed point problems: an introduction Ferreira, Paulo J. S. G. |
title_short |
Fixed point problems: an introduction |
title_full |
Fixed point problems: an introduction |
title_fullStr |
Fixed point problems: an introduction |
title_full_unstemmed |
Fixed point problems: an introduction |
title_sort |
Fixed point problems: an introduction |
author |
Ferreira, Paulo J. S. G. |
author_facet |
Ferreira, Paulo J. S. G. |
author_role |
author |
dc.contributor.author.fl_str_mv |
Ferreira, Paulo J. S. G. |
description |
This paper surveys a number of fundamental results on the existence and uniqueness of fixed points for certain classes of possibly nonlinear operators. I do not try to be exhaustive, but merely to present the results that are more useful in the context of signal and image reconstruction. Some specific aspects pertaining to linear operators, and linear operators in finite dimensional spaces, are also discussed. It is shown that the set of fixed points of a nonexpansive operator is either empty or convex. Under rather general conditions this shows that the minimum norm solution of an operator equation of the form x = Ax exists and is unique, provided that is nonexpansive. This is a new result, which has interesting practical consequences in signal and image reconstruction problems and in other engineering applications. |
publishDate |
1996 |
dc.date.none.fl_str_mv |
1996-01-01T00:00:00Z |
dc.type.driver.fl_str_mv |
journal article info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://proa.ua.pt/index.php/revdeti/article/view/19815 oai:proa.ua.pt:article/19815 |
url |
https://proa.ua.pt/index.php/revdeti/article/view/19815 |
identifier_str_mv |
oai:proa.ua.pt:article/19815 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://proa.ua.pt/index.php/revdeti/article/view/19815 https://proa.ua.pt/index.php/revdeti/article/view/19815/14379 |
dc.rights.driver.fl_str_mv |
https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
UA Editora |
publisher.none.fl_str_mv |
UA Editora |
dc.source.none.fl_str_mv |
Eletrónica e Telecomunicações; Vol 1 No 6 (1996); 505-514 Eletrónica e Telecomunicações; vol. 1 n.º 6 (1996); 505-514 2182-9772 1645-0493 reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799130545165172736 |