Başarır, MetinKayıkçı, Mustafa2020-04-302020-04-3020091029-242Xhttps://doi.org/10.1155/2009/385029https://hdl.handle.net/20.500.12684/3935Basarir, Metin/0000-0002-4341-4399WOS: 000270606300001We introduce the generalized Riesz difference sequence space r(q)(p, B-m) which is defined by r(q)(p, B-m) = {x = (x(k)) is an element of w : B(m)x is an element of r(q)(p)} where r(q)(p) is the Riesz sequence space defined by Altay and Basar. We give some topological properties, compute the alpha_, beta_ 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 r(q)(p, B-m) and we have proved that this sequence space has property (beta) for p(k) >= 1. Copyright (C) 2009 M. Basarir and M. Kayikci.en10.1155/2009/385029info:eu-repo/semantics/openAccessArticleWOS:000270606300001Q2Q2