On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field
The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical rea...
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| Main Authors: | , , |
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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/10.1155/2015/416906 |
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| _version_ | 1832556083359514624 |
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| author | Uğur Kadak Murat Kirişci Ahmet Faruk Çakmak |
| author_facet | Uğur Kadak Murat Kirişci Ahmet Faruk Çakmak |
| author_sort | Uğur Kadak |
| collection | DOAJ |
| description | The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are ⋆-complete. By using the notion of multiplier sequence, the α-, β-, and γ-duals of certain paranormed spaces have been computed and their basis has been constructed. |
| format | Article |
| id | doaj-art-a783c08829724dd4a7a4ffef80cbd4d4 |
| 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-a783c08829724dd4a7a4ffef80cbd4d42025-02-03T05:46:24ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/416906416906On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex FieldUğur Kadak0Murat Kirişci1Ahmet Faruk Çakmak2Department of Mathematics, Faculty of Sciences and Arts, Bozok University, 66200 Yozgat, TurkeyDepartment of Mathematical Education, Hasan Ali Yücel Education Faculty, Istanbul University, 34470 Istanbul, TurkeyDepartment of Mathematical Engineering, Yıldız Technical University, 80750 Istanbul, TurkeyThe studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are ⋆-complete. By using the notion of multiplier sequence, the α-, β-, and γ-duals of certain paranormed spaces have been computed and their basis has been constructed.http://dx.doi.org/10.1155/2015/416906 |
| spellingShingle | Uğur Kadak Murat Kirişci Ahmet Faruk Çakmak On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field Journal of Function Spaces |
| title | On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field |
| title_full | On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field |
| title_fullStr | On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field |
| title_full_unstemmed | On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field |
| title_short | On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field |
| title_sort | on the classical paranormed sequence spaces and related duals over the non newtonian complex field |
| url | http://dx.doi.org/10.1155/2015/416906 |
| work_keys_str_mv | AT ugurkadak ontheclassicalparanormedsequencespacesandrelateddualsoverthenonnewtoniancomplexfield AT muratkirisci ontheclassicalparanormedsequencespacesandrelateddualsoverthenonnewtoniancomplexfield AT ahmetfarukcakmak ontheclassicalparanormedsequencespacesandrelateddualsoverthenonnewtoniancomplexfield |