On the Paranormed Space of Bounded Variation Double Sequences


Yeşilkayagil M., Başar F.

Bulletin of the Malaysian Mathematical Sciences Society, cilt.43, sa.3, ss.2701-2712, 2020 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s40840-019-00829-2
  • Dergi Adı: Bulletin of the Malaysian Mathematical Sciences Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.2701-2712
  • Anahtar Kelimeler: Alpha, beta and gamma duals, Double sequences, Double series, Matrix domain of four-dimensional matrices, Matrix transformations, Summability theory
  • Uşak Üniversitesi Adresli: Evet

Özet

In this study, as the domain of four-dimensional backward difference matrix in the space Lu(t) , we introduce the complete paranormed space BV(t) of bounded variation double sequences and examine some properties of that space. Also, we determine the γ-dual and β(ϑ) -dual of the space BV(t). Finally, we characterize the classes (BV(t) : Mu) , (BV(t) : Cϑ) and (Lu(t) : μ) with μ∈ { BS, CSϑ, Mu(Δ) , Cϑ(Δ) } , where Mu(Δ) and Cϑ(Δ) denote the spaces of all double sequences whose Δ -transforms are in the spaces Mu and Cϑ, respectively.