Matrix Transformations Involving Generalized Almost Convergent Sequences

SAVAŞ E., Zeltser M.

Analysis Mathematica, vol.45, no.2, pp.413-441, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1007/s10476-019-0733-3
  • Journal Name: Analysis Mathematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.413-441
  • Keywords: almost convergence, Maddox sequence space, matrix transformation
  • Uşak University Affiliated: Yes

Abstract

In [7] Maddox generalized the spaces c0, c, ℓ1, ℓ∞ by adding powers pk (k ∈ ℕ) in the definitions of the spaces to the terms of the elements of the sequences (xk). Using the ideas of Maddox, Nanda [13] defined generalizations f(p) and f0(p) of the spaces of all almost convergent sequences f and of all sequences f0 almost convergent to 0. In [13] and [14] he characterized some classes of matrix transformations involving theses spaces and Maddox’s sequence spaces. We have discovered that almost all results in [13] and [14] are faulty. In this paper we give corresponding counterexamples and prove the correct results. Moreover we prove them in more general settings.