Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series
The main purpose of this study is to introduce the spaces csλ, cs0λ, and bsλ which are BK-spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spaces cs, cs0, and bs, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spaces csλ an...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/458324 |
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| author | Meltem Kaya Hasan Furkan |
| author_facet | Meltem Kaya Hasan Furkan |
| author_sort | Meltem Kaya |
| collection | DOAJ |
| description | The main purpose of this study is to introduce the spaces csλ, cs0λ, and bsλ which are BK-spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spaces cs, cs0, and bs, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spaces csλ and cs0λ have been constructed and the α-, β-, and γ-duals of these spaces have been computed. Besides, we characterize some matrix classes from the spaces csλ, cs0λ, and bsλ to the spaces lp, c, and c0, where 1≤p≤∞. Finally, we examine some geometric properties of these spaces as Gurarǐ’s modulus of convexity, property m∞, property (M), property WORTH, nonstrict Opial property, and weak fixed point property. |
| format | Article |
| id | doaj-art-7a22bee3c78f41f1b61175d31fa550b8 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7a22bee3c78f41f1b61175d31fa550b82025-02-03T01:20:55ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/458324458324Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded SeriesMeltem Kaya0Hasan Furkan1Department of Mathematics, Kahramanmaraş Sütçü İmam University, 46100 Kahramanmaraş, TurkeyDepartment of Mathematics, Kahramanmaraş Sütçü İmam University, 46100 Kahramanmaraş, TurkeyThe main purpose of this study is to introduce the spaces csλ, cs0λ, and bsλ which are BK-spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spaces cs, cs0, and bs, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spaces csλ and cs0λ have been constructed and the α-, β-, and γ-duals of these spaces have been computed. Besides, we characterize some matrix classes from the spaces csλ, cs0λ, and bsλ to the spaces lp, c, and c0, where 1≤p≤∞. Finally, we examine some geometric properties of these spaces as Gurarǐ’s modulus of convexity, property m∞, property (M), property WORTH, nonstrict Opial property, and weak fixed point property.http://dx.doi.org/10.1155/2015/458324 |
| spellingShingle | Meltem Kaya Hasan Furkan Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series Journal of Function Spaces |
| title | Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series |
| title_full | Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series |
| title_fullStr | Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series |
| title_full_unstemmed | Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series |
| title_short | Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series |
| title_sort | some topological and geometric properties of some new spaces of λ convergent and bounded series |
| url | http://dx.doi.org/10.1155/2015/458324 |
| work_keys_str_mv | AT meltemkaya sometopologicalandgeometricpropertiesofsomenewspacesoflconvergentandboundedseries AT hasanfurkan sometopologicalandgeometricpropertiesofsomenewspacesoflconvergentandboundedseries |