On some new double sequence spaces defined by a modulus


Savas E.

APPLIED MATHEMATICS AND COMPUTATION, vol.187, no.1, pp.417-424, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 187 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.amc.2006.08.141
  • Title of Journal : APPLIED MATHEMATICS AND COMPUTATION
  • Page Numbers: pp.417-424

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 is an element of s" : P - lim(m,n)Sigma(infinity infinity)(k,l=0,0)a(m,n,k,l)f(vertical bar x(sigma k(p),sigma l(q))vertical bar)(Pk,l) = 0}, {x is an element of s" : P - lim(m,n)Sigma(infinity infinity)(k,l=0,0)a(m,n,k,l)f(vertical bar x(sigma k(p),sigma l(p)) - Le vertical bar)(Pk,l) = 0, for some L}, and {x is an element of s" : sup(m,n,p,q)Sigma(infinity infinity)(k,l=0,0)a(m,n,k,l)f(vertical bar x(sigma(p)sigma l(q))vertical bar)(Pk,l) < infinity} 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 sigma-statistical convergence. (c) 2006 Elsevier Inc. All rights reserved.