On the Generalized Bm -Riesz Difference Sequence Space and [beta] -Property

We introduce the generalized Riesz difference sequence space [superscript]rq[/superscript] (p,[superscript]Bm[/superscript] ) which is defined by [superscript]rq[/superscript] (p,[superscript]Bm[/superscript] )={x=([subscript]xk[/subscript] )∈w:[superscript]Bm[/superscript] x∈[superscript]rq[/superscript] (p)} where [superscript]rq[/superscript] (p) is the Riesz sequence space defined by Altay and Basar. 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 [superscript]rq[/superscript] (p,[superscript]Bm[/superscript] ) and we have proved that this sequence space has property (β) for [subscript]pk[/subscript] ≥1 .