A new look at the classical sequence spaces by using multiplicative calculus


GÜREFE Y., Kadak Ǔ., Misirli E., Kurdi A.

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, vol.78, no.2, pp.9-20, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 78 Issue: 2
  • Publication Date: 2016
  • Journal Name: UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.9-20
  • Keywords: Complete metric space, Metric topology, Multiplicative calculus, Sequence spaces
  • Uşak University Affiliated: Yes

Abstract

The important point to be noted on 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. In the present paper, some fundamental theorems and notions of the classical calculus are in- Terpreted from the view point of multiplicative calculus and the analogies between them are given. We propose a concrete approach based on some topological prop- erties with respect to the multiplicative calculus. Finally, we give ∗-completeness results on some sets of specific sequences.