Topological Quasilinear Spaces
We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets a...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/951374 |
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| _version_ | 1832560481994276864 |
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| author | Yılmaz Yılmaz Sümeyye Çakan Şahika Aytekin |
| author_facet | Yılmaz Yılmaz Sümeyye Çakan Şahika Aytekin |
| author_sort | Yılmaz Yılmaz |
| collection | DOAJ |
| description | We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces. |
| format | Article |
| id | doaj-art-951668135d7e4b9eb9b4dbc351af86cd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-951668135d7e4b9eb9b4dbc351af86cd2025-02-03T01:27:26ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/951374951374Topological Quasilinear SpacesYılmaz Yılmaz0Sümeyye Çakan1Şahika Aytekin2Department of Mathematics, Inonu University, 44280 Malatya, TurkeyDepartment of Mathematics, Inonu University, 44280 Malatya, TurkeyDepartment of Mathematics, Inonu University, 44280 Malatya, TurkeyWe introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.http://dx.doi.org/10.1155/2012/951374 |
| spellingShingle | Yılmaz Yılmaz Sümeyye Çakan Şahika Aytekin Topological Quasilinear Spaces Abstract and Applied Analysis |
| title | Topological Quasilinear Spaces |
| title_full | Topological Quasilinear Spaces |
| title_fullStr | Topological Quasilinear Spaces |
| title_full_unstemmed | Topological Quasilinear Spaces |
| title_short | Topological Quasilinear Spaces |
| title_sort | topological quasilinear spaces |
| url | http://dx.doi.org/10.1155/2012/951374 |
| work_keys_str_mv | AT yılmazyılmaz topologicalquasilinearspaces AT sumeyyecakan topologicalquasilinearspaces AT sahikaaytekin topologicalquasilinearspaces |