Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field
The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus....
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/438924 |
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| author | Uğur Kadak |
| author_facet | Uğur Kadak |
| author_sort | Uğur Kadak |
| collection | DOAJ |
| description | The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness. |
| format | Article |
| id | doaj-art-4fdffb34a1d848bc8c8e5bc14c77b105 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-4fdffb34a1d848bc8c8e5bc14c77b1052025-02-03T06:06:57ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/438924438924Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex FieldUğur Kadak0Department of Mathematics, Faculty of Science, Gazi University, 06100 Ankara, TurkeyThe important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Therefore the reader may be surprised to learn that there is a uniform relationship between the corresponding operators of this calculus and the classical calculus. Several basic concepts based on non-Newtonian calculus are presented by Grossman (1983), Grossman and Katz (1978), and Grossman (1979). Following Grossman and Katz, in the present paper, we introduce the sets of bounded, convergent, null series and p-bounded variation of sequences over the complex field C* and prove that these are complete. We propose a quite concrete approach based on the notion of Köthe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Köthe space and solidness.http://dx.doi.org/10.1155/2014/438924 |
| spellingShingle | Uğur Kadak Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field The Scientific World Journal |
| title | Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field |
| title_full | Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field |
| title_fullStr | Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field |
| title_full_unstemmed | Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field |
| title_short | Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field |
| title_sort | determination of the kothe toeplitz duals over the non newtonian complex field |
| url | http://dx.doi.org/10.1155/2014/438924 |
| work_keys_str_mv | AT ugurkadak determinationofthekothetoeplitzdualsoverthenonnewtoniancomplexfield |