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The Scientific World Journal
Volume 2014, Article ID 438924, 10 pages
http://dx.doi.org/10.1155/2014/438924
Research Article

Determination of the Köthe-Toeplitz Duals over the Non-Newtonian Complex Field

1Department of Mathematics, Faculty of Science, Gazi University, 06100 Ankara, Turkey
2Department of Mathematics, Faculty of Science, Bozok University, 66100 Yozgat, Turkey

Received 3 February 2014; Accepted 9 March 2014; Published 16 June 2014

Academic Editors: J. Banas and M. Mursaleen

Copyright © 2014 Uğur Kadak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 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.