On some new double sequence spaces defined by a modulus

Savaş E.

Applied Mathematics and Computation, vol.187, no.1 SPEC. ISS., pp.417-424, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 187 Issue: 1 SPEC. ISS.
  • Publication Date: 2007
  • Doi Number: 10.1016/j.amc.2006.08.141
  • Journal Name: Applied Mathematics and Computation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.417-424
  • Keywords: Double sequences, Modulus functions, P-convergent
  • Uşak University Affiliated: No

Abstract

In this paper our purpose is to extend some results known in the literature for ordinary (single) sequences to multiply sequences of real and complex numbers. This will be accomplished by presenting the following sequence spaces: {x ∈ s″ : P - limm, n ∑k, l = 0, 0 ∞, ∞ am, n, k, l f (| xσk (p), σl (q) |)pk, l = 0}, {Mathematical expression} and {Mathematical expression} where f is a modulus function, uniformly in (p, q) and A is a nonnegative RH-regular summability matrix method. In addition, we shall give double σ-statistical convergence. © 2006 Elsevier Inc. All rights reserved.