On some new double sequence spaces defined by a modulus


Savas E.

APPLIED MATHEMATICS AND COMPUTATION, cilt.187, ss.417-424, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 187 Konu: 1
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.amc.2006.08.141
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Sayfa Sayıları: ss.417-424

Özet

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.