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


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Kadak U.

SCIENTIFIC WORLD JOURNAL, 2014 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1155/2014/438924
  • Dergi Adı: SCIENTIFIC WORLD JOURNAL

Özet

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 Kothe-Toeplitz duals with respect to the non-Newtonian calculus. Finally, we derive some inclusion relationships between Kothe space and solidness.