On an equivalence of topological vector space valued cone metric spaces and metric spaces

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dc.authorid0000-0001-7344-5826en_US
dc.contributor.authorCakalli, Huseyin
dc.contributor.authorSonmez, Ayse
dc.contributor.authorGenc, Cigdem
dc.date.accessioned2024-07-12T21:45:03Z
dc.date.available2024-07-12T21:45:03Z
dc.date.issued2012en_US
dc.departmentMaltepe Üniversitesien_US
dc.description.abstractScalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied by Du (2010) [14] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper, we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable, prove a completion theorem, and also obtain some more results in topological vector space valued cone normed spaces. (C) 2011 Elsevier Ltd. All rights reserved.en_US
dc.identifier.doi10.1016/j.aml.2011.09.029
dc.identifier.endpage433en_US
dc.identifier.issn0893-9659
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-80955172793en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage429en_US
dc.identifier.urihttps://dx.doi.org/10.1016/j.aml.2011.09.029
dc.identifier.urihttps://hdl.handle.net/20.500.12415/7785
dc.identifier.volume25en_US
dc.identifier.wosWOS:000298201700037en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherPERGAMON-ELSEVIER SCIENCE LTDen_US
dc.relation.ispartofAPPLIED MATHEMATICS LETTERSen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKY00303
dc.subjectTVS-cone metric spaceen_US
dc.subjectGeneralized TVS-cone metric spaceen_US
dc.subjectCone Banach spacesen_US
dc.subjectSet-valued operatorsen_US
dc.titleOn an equivalence of topological vector space valued cone metric spaces and metric spacesen_US
dc.typeArticle
dspace.entity.typePublication

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