tailieunhanh - Báo cáo hóa học: " Research Article Solvability Criteria for Some Set-Valued Inequality Systems"

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 Solvability Criteria for Some Set-Valued Inequality Systems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 543061 17 pages doi 2010 543061 Research Article Solvability Criteria for Some Set-Valued Inequality Systems Yingfan Liu Department of Mathematics College of Science Nanjing University of Posts and Telecommunications Nanjing 210009 China Correspondence should be addressed to Yingfan Liu yingfanliu@ Received 23 May 2010 Accepted 9 July 2010 Academic Editor Qamrul Hasan Ansari Copyright 2010 Yingfan Liu. 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. Arising from studying some multivalued von Neumann model three set-valued inequality systems are introduced and two solvability questions are considered. By constructing some auxiliary functions and studying their minimax and saddle-point properties solvability criteria composed of necessary and sufficient conditions regarding these inequality systems are obtained. 1. Introduction Arising from considering some multivalued von Neumann model this paper aims to study three set-valued inequality systems and try to find their solvability criteria. Before starting with this subject we need to review some necessary backgrounds as follows. We denote by Rk Rk II II the k-dimensional Euclidean space Rk Rk its dual and the duality pairing on Rk Rk moreover we denote that Rk x e Rk xi 0 Vi and int Rk is its interior. We also define or in Rk by x y o x - y e Rk or by x y o x - y e int Rk . It is known that the generalized linear or nonlinear von Neumann model which is composed of an inequality system and a growth factor problem described by a 3x e X Bx - Ax c respectively b A 1 . 3x e X Bx lAx c is one of the most important issues in the input-output analysis 1-3 where c e Rm X c Rn m may not be equal to n and B A are two nonnegative or positive maps .

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