Normed proper quasilinear spaces

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dc.authoridÇAKAN, Sümeyye/0000-0001-8761-8564
dc.authorwosidYilmaz, Yilmaz/A-9582-2018
dc.authorwosidÇAKAN, Sümeyye/ABH-4275-2020
dc.contributor.authorCakan, Sumeyye
dc.contributor.authorYilmaz, Yilmaz
dc.date.accessioned2024-08-04T20:40:20Z
dc.date.available2024-08-04T20:40:20Z
dc.date.issued2015
dc.departmentİnönü Üniversitesien_US
dc.description.abstractThe fundamental deficiency in the theory of quasilinear spaces, introduced by Aseev [S. M. Aseev, Trudy Mat. Inst. Steklov., 167 (1985), 25-52], is the lack of a satisfactory definition of linear dependence-independence and basis notions. Perhaps, this is the most important obstacle in the progress of normed quasilinear spaces. In this work, after giving the notions of quasilinear dependence-independence and basis presented by Banazili[H. K. Banazili, M. Sc. Thesis, Malatya, Turkey (2014)] and Cakan [S. Cakan, Ph.D. Seminar, Malatya, Turkey (2012)], we introduce the concepts of regular and singular dimension of a quasilinear space. Also, we present a new notion namely proper quasilinear spaces and show that these two kind dimensions are equivalent in proper quasilinear spaces. Moreover, we try to explore some properties of finite regular and singular dimensional normed quasilinear spaces. We also obtain some results about the advantages of features of proper quasilinear spaces. (C) 2015 All rights reserved.en_US
dc.identifier.doi10.22436/jnsa.008.05.32
dc.identifier.endpage836en_US
dc.identifier.issn2008-1898
dc.identifier.issn2008-1901
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-84937136062en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage816en_US
dc.identifier.urihttps://doi.org/10.22436/jnsa.008.05.32
dc.identifier.urihttps://hdl.handle.net/11616/96865
dc.identifier.volume8en_US
dc.identifier.wosWOS:000359986800032en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherInt Scientific Research Publicationsen_US
dc.relation.ispartofJournal of Nonlinear Sciences and Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectQuasilinear spacesen_US
dc.subjectHausdorff metricen_US
dc.subjectregular dimensionen_US
dc.subjectsingular dimensionen_US
dc.subjectfloor of an elementen_US
dc.subjectproper setsen_US
dc.subjectproper quasilinear spacesen_US
dc.titleNormed proper quasilinear spacesen_US
dc.typeArticleen_US

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