International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 701-706
doi:10.1155/S0161171298000970

Difference sequence spaces

A. K. Gaur1 and Mursaleen2

1Department of Mathematics, Duquesne University, Pittsburgh 15282, PA, USA
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Received 17 April 1996; Revised 29 July 1996

Copyright © 1998 A. K. Gaur and Mursaleen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In [1] Sr(Δ):={x=(xk):(kr|Δxk|)k=1∞∈c0} for r≥1 is studied. In this paper, we generalize this space to Sr(p,Δ) for a sequence of strictly positive reals. We give a characterization of the matrix classes (Sr(p,Δ),ℓ∞) and (Sr(p,Δ),ℓ1).