tailieunhanh - Báo cáo hóa học: " Research Article On the Generalized Bm -Riesz Difference Sequence Space and β-Property"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Generalized Bm -Riesz Difference Sequence Space and β-Property | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 3850229 18 pages doi 2009 385029 Research Article On the Generalized Bm-Riesz Difference Sequence Space and -Property Metin Basarir1 and Mustafa Kayikci2 1 Department of Mathematics Sakarya University 54187 Sakarya Turkey 2 Duzce MYO Duzce University 81010 Duzce Turkey Correspondence should be addressed to Metin Basarir basarir@ Received 1 May 2009 Accepted 17 July 2009 Recommended by Ramm Mohapatra We introduce the generalized Riesz difference sequence space rq p Bm which is defined by rq p Bm x xk e w Bmx e rq p where rq p is the Riesz sequence space defined by Altay and Basar. We give some topological properties compute the a_ p_ 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 P for Pk 1. Copyright 2009 M. Baẹarir and M. Kayikci. 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. 1. Introduction Let w be the space of all real valued sequences. We write lTO c c0 for the sequence spaces of all bounded convergent and null sequences respectively. Also by cs l1 and lp we denote the sequence spaces of all convergent absolutely and p-absolutely convergent series respectively where 1 p TO. Let qk be a sequence of positive numbers and n Qn qk n e N . k 0 Then the matrix Rq r k of the Riesz mean R qn which is triangle limitation matrix is given by q qk 0 k IM rf_ Qn nk 0 fk n . It is well known that the matrix Rq r k is regular if and only if Qn TO as n TO. 2 Journal of Inequalities and Applications Altay and Basar 1 2 introduced the Riesz sequence space rq p rZ p rq p .