On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field

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Kadak U., KİRİŞCİ M., ÇAKMAK A. F.

JOURNAL OF FUNCTION SPACES, vol.2015, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2015
  • Publication Date: 2015
  • Doi Number: 10.1155/2015/416906
  • Journal Name: JOURNAL OF FUNCTION SPACES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Yozgat Bozok University Affiliated: Yes

Abstract

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 star-complete. By using the notion of multiplier sequence, the alpha-, beta-, and gamma-duals of certain paranormed spaces have been computed and their basis has been constructed.