Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 385029, 18 pages
Research Article

On the Generalized Bm-Riesz Difference Sequence Space and β-Property

1Department of Mathematics, Sakarya University, 54187 Sakarya, Turkey
2Duzce MYO, Duzce University, 81010 Duzce, Turkey

Received 1 May 2009; Accepted 17 July 2009

Academic Editor: Ramm Mohapatra

Copyright © 2009 Metin Başarir and Mustafa Kayikçi. 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.


We introduce the generalized Riesz difference sequence space rq(p,Bm) which is defined by rq(p,Bm)={x=(xk)w:Bmxrq(p)} where rq(p) is the Riesz sequence space defined by Altay and Başar. We give some topological properties, compute the α_,β_ duals, and determine the Schauder basis of this space. Finally; we study the characterization of some matrix mappings on this sequence space. At the end of the paper, we investigate some geometric properties of rq(p,Bm) and we have proved that this sequence space has property (β) for pk1.