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Báo cáo hóa học: " Research Article Some Geometric Inequalities in a New Banach Sequence Space"

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 Some Geometric Inequalities in a New Banach Sequence Space | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 86757 6 pages doi 10.1155 2007 86757 Research Article Some Geometric Inequalities in a New Banach Sequence Space M. Mursaleen Rifat Colak and Mikail Et Received 11 July 2007 Accepted 18 November 2007 Recommended by Peter Yu Hin Pang The difference sequence space m 0 p A r which is a generalization of the space m 0 introduced and studied by Sargent 1960 was defined by Colak and Et 2005 . In this paper we establish some geometric inequalities for this space. Copyright 2007 M. Mursaleen et al. 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 and preliminaries Let C denote the space whose elements are finite sets of distinct positive integers. Given an element Ơ e we write c ơ for the sequence cn ơ such that cn ơ 1 for n e Ơ and cn ơ 0 otherwise. Further s jơ e cn ơ si 1.1 n 1 -1 that is r is the set of those Ơ whose support has cardinality at most s where s is a natural number. Let w be the set of all real sequences and o u n e w 01 0 Vộk 0 v 0 k 1 2 . 1.2 n k where Vộk ộk - ộk-r For Ộ e o Sargent 1 introduced the following sequence space mf AA J VJ fv.J 1.4 7 Q11T1 Q11T1 Ỉ I V. I fV f 1 -V x x e w sup sup x I x t- . . nn I s 1 a e A sneơ 2 Journal of Inequalities and Applications In 2 the space m Y has been considered for matrix transformations and in 3 some of its geometric properties have been considered. Tripathy and Sen 4 extended m Y to m Y p 1 p o. Recently Colak and Et 5 defined the space m Y p A r by using the idea of difference sequences see 6-8 . Let r be a positive integer throughout. The operators A r 2 r w w are defined by A 1 k Ax k Xk - Xk 1 X 1 x k 2x k Xj k 1 2 . j k A r A 1 o A r-1 2 r 2 1 o E r-1 r 2 2 r o A ri A ri o E r id the identity on w. For 0 p o the space m Y p A r is .