Best proximity pair results for relatively nonexpansive mappings in geodesic spaces
Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively nonexpansive if d(T x, T y) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, T x) = dist(A,B). In this work, we extend the results given in [...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43080 |
| Acceso en línea: | http://hdl.handle.net/11441/43080 https://doi.org/10.1080/01630563.2014.895762 |
| Access Level: | acceso abierto |
| Palabra clave: | Relatively nonexpansive mapping Best proximity pair Best proximity point Proximal normal structure Busemann convexity |
| id |
ES_acc5045eebbadc85c4e7568f4cbe8cea |
|---|---|
| oai_identifier_str |
oai:idus.us.es:11441/43080 |
| network_acronym_str |
ES |
| network_name_str |
España |
| repository_id_str |
|
| spelling |
Best proximity pair results for relatively nonexpansive mappings in geodesic spacesFernández León, AuroraNicolae, AdrianaRelatively nonexpansive mappingBest proximity pairBest proximity pointProximal normal structureBusemann convexityGiven A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively nonexpansive if d(T x, T y) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, T x) = dist(A,B). In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171, 283–293 (2005)] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in A × B of a pair of best proximity points.Marcel. DekkerDidáctica de las Matemáticas2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/43080https://doi.org/10.1080/01630563.2014.895762reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNumerical functional analysis and optimization, 35 (11), 1399-1418.http://dx.doi.org/10.1080/01630563.2014.895762info:eu-repo/semantics/openAccessoai:idus.us.es:11441/430802026-06-17T12:51:07Z |
| dc.title.none.fl_str_mv |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| title |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| spellingShingle |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces Fernández León, Aurora Relatively nonexpansive mapping Best proximity pair Best proximity point Proximal normal structure Busemann convexity |
| title_short |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| title_full |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| title_fullStr |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| title_full_unstemmed |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| title_sort |
Best proximity pair results for relatively nonexpansive mappings in geodesic spaces |
| dc.creator.none.fl_str_mv |
Fernández León, Aurora Nicolae, Adriana |
| author |
Fernández León, Aurora |
| author_facet |
Fernández León, Aurora Nicolae, Adriana |
| author_role |
author |
| author2 |
Nicolae, Adriana |
| author2_role |
author |
| dc.contributor.none.fl_str_mv |
Didáctica de las Matemáticas |
| dc.subject.none.fl_str_mv |
Relatively nonexpansive mapping Best proximity pair Best proximity point Proximal normal structure Busemann convexity |
| topic |
Relatively nonexpansive mapping Best proximity pair Best proximity point Proximal normal structure Busemann convexity |
| description |
Given A and B two nonempty subsets in a metric space, a mapping T : A ∪ B → A ∪ B is relatively nonexpansive if d(T x, T y) ≤ d(x, y) for every x ∈ A, y ∈ B. A best proximity point for such a mapping is a point x ∈ A ∪ B such that d(x, T x) = dist(A,B). In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171, 283–293 (2005)] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in A × B of a pair of best proximity points. |
| publishDate |
2014 |
| dc.date.none.fl_str_mv |
2014 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion |
| format |
article |
| status_str |
submittedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11441/43080 https://doi.org/10.1080/01630563.2014.895762 |
| url |
http://hdl.handle.net/11441/43080 https://doi.org/10.1080/01630563.2014.895762 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Numerical functional analysis and optimization, 35 (11), 1399-1418. http://dx.doi.org/10.1080/01630563.2014.895762 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Marcel. Dekker |
| publisher.none.fl_str_mv |
Marcel. Dekker |
| dc.source.none.fl_str_mv |
reponame:idUS. Depósito de Investigación de la Universidad de Sevilla instname:Universidad de Sevilla (US) |
| instname_str |
Universidad de Sevilla (US) |
| reponame_str |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| collection |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| repository.name.fl_str_mv |
|
| repository.mail.fl_str_mv |
|
| _version_ |
1869416383185420288 |
| score |
15,300724 |