Some Notes on the New Sequence Space 𝒃𝒑𝒓𝒔(𝑫)

SÖNMEZ A.

Gazi University Journal of Science, vol.33, no.2, pp.476-490, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.35378/gujs.522691
  • Journal Name: Gazi University Journal of Science
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.476-490
  • Keywords: Matrix transformation, Matrix domain, Schauder basis, alpha-, beta- and gamma-duals, INCLUDE, L(P)
  • Erciyes University Affiliated: Yes

Abstract

In this paper, we describe the sequence space b(p)(r,s)(D) originated by the composition of the Binomial matrix and generalized second order difference (triple band) matrix and indicate that the space b(p)(r,s)(D) is linearly isomorphic to the space l(p), where 1 <= p < infinity. Moreover, we obtain some inclusion relations and Schauder basis of the space b(p)(r,s)(D). We also pinpoint alpha-, beta- and gamma-duals of the space b(p)(r,s)(D) Finally, we classify some matrix classes related to the space b(p)(r,s)(D).