Domain of q-Cesaro Matrix in Hahn Sequence Space h(d) and the Space bv of the Sequences of Bounded Variation

Yayinga T., KİRİŞCİ M., Hazarika B., Tug O.

FILOMAT, vol.36, no.19, pp.6427-6441, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 19
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2219427y
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.6427-6441
  • Istanbul University Affiliated: No

Abstract

Let h(d)= {f = (f(k)) is an element of omega: Sigma(k) d(k)| f(k) - f(k+1)| < infinity} boolean AND c(0), where d = (d(k)) is an unbounded and monotonic increasing sequence of positive reals. We study the matrix domains h(d)(C-q) = (h(d))C-q and bv(C-q) = (bv) C-q, where C-q is the q-Cesaro matrix, 0 < q < 1. Apart from the inclusion relations and Schauder basis, we compute alpha-, beta- and gamma-duals of the spaces h(d)(C-q) and bv(C-q). We state and prove theorems concerning characterization of matrix classes from the spaces h(d)(C-q) and bv(C-q) to any one of the space l(infinity), c, c(0) or l(1). Finally, we obtain certain identities concerning characterization of compact operators using Hausdorff measure of non-compactness in the space h(d)(C-q).