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 Some Generalized B m-Difference Riesz Sequence Spaces and Uniform Opial Property | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 485730 17 pages doi 2011 485730 Research Article On Some Generalized Bm-Difference Riesz Sequence Spaces and Uniform Opial Property Metin Basarir and Mahpeyker Ozturk Department of Mathematics Sakarya University 54187 Sakarya Turkey Correspondence should be addressed to Metin Baẹarir basarir@ Received 29 November 2010 Accepted 18 January 2011 Academic Editor Radu Precup Copyright 2011 M. Basarir and M. Ozturk. 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 define the new generalized difference Riesz sequence spaces rf p Bm rC p Bm and rC p Bm which consist of all the sequences whose Bm-transforms are in the Riesz sequence spaces rf p rq p and rC p respectively introduced by Altay and Basar 2006 . We examine some topological properties and compute the a- Ộ- and p-duals of the spaces rf p Bm rC p Bm and rC p Bm . Finally we determine the necessary and sufficient conditions on the matrix transformation from the spaces rf p Bm rC p Bm and rC p Bm to the spaces lf and c and prove that sequence spaces r0 p Bm and rC p Bm have the uniform Opial property for pk 1 for all k eN. 1. Introduction Let w be the space of real sequences. We write lf c c0 for the sequence spaces of all bounded convergent and null sequences respectively. Also by bs cs and l1 we denote the sequence spaces of all bounded convergent and absolutely convergent series respectively. A linear topological space X over the real field R is said to be a paranormed space if there is a subadditive function g X R such that g 0 0 g x g -x and scalar multiplication is continuous that is an - a 0 and g xn - x 0 imply g anxn - ax 0 for all a s in R and all x s in X where 0 is the zero vector in the linear space X. Assume here and after .
