Double sequence spaces defined by a modulus

Savaş E., Patterson R. F.

Mathematica Slovaca, vol.61, no.2, pp.245-256, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.2478/s12175-011-0009-2
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.245-256
  • Keywords: double sequences, modulus functions, P-convergent
  • Uşak University Affiliated: No

Abstract

This paper begins with new definitions for double sequence spaces. These new definitions are constructed, in general, by combining modulus function and nonnegative four-dimensional matrix. We use these definitions to establish inclusion theorems between various sequence spaces such as: If A = (am,n,k,l) be a nonnegative four-dimensional matrix such that and let f be a modulus, then ω″(A, f) ⊂ ω″∞(A, f) and ω″0(A, f) ⊂ ω″∞(A, f). © 2011 Versita Warsaw and Springer-Verlag Wien.