TAILIEUCHUNG - Báo cáo hóa học: " Research Article Connectedness and Compactness of Weak Efficient Solutions for Set-Valued Vector "

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 Connectedness and Compactness of Weak Efficient Solutions for Set-Valued Vector | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 581849 15 pages doi 2008 581849 Research Article Connectedness and Compactness of Weak Efficient Solutions for Set-Valued Vector Equilibrium Problems Bin Chen Xun-Hua Gong and Shu-Min Yuan Department of Mathematics Nanchang University Nanchang 330047 China Correspondence should be addressed to Xun-Hua Gong xunhuagong@ Received 1 November 2007 Revised 17 July 2008 Accepted 5 September 2008 Recommended by C. E. Chidume We study the set-valued vector equilibrium problems and the set-valued vector Hartman-Stampacchia variational inequalities. We prove the existence of solutions of the two problems. In addition we prove the connectedness and the compactness of solutions of the two problems in normed linear space. Copyright 2008 Bin Chen 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 We know that one of the important problems of vector variational inequalities and vector equilibrium problems is to study the topological properties of the set of solutions. Among its topological properties the connectedness and the compactness are of interest. Recently Lee et al. 1 and Cheng 2 have studied the connectedness of weak efficient solutions set for single-valued vector variational inequalities in finite dimensional Euclidean space. Gong 3-5 has studied the connectedness of the various solutions set for single-valued vector equilibrium problem in infinite dimension space. The set-valued vector equilibrium problem was introduced by Ansari et al. 6 . Since then Ansari and Yao 7 Konnov and Yao 8 Fu 9 Hou et al. 10 Tan 11 Peng et al. 12 Ansari and Flores-Bazan 13 Lin et al. 14 and Long et al. 15 have studied the existence of solutions for set-valued vector equilibrium and set-valued vector .

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