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Báo cáo hóa học: " Research Article Upper Semicontinuity of Solution Maps for a Parametric Weak Vector Variational Inequality"

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 Upper Semicontinuity of Solution Maps for a Parametric Weak Vector Variational Inequality | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 482726 6 pages doi 10.1155 2010 482726 Research Article Upper Semicontinuity of Solution Maps for a Parametric Weak Vector Variational Inequality Z. M. Fang and S. J. Li College of Mathematics and Science Chongqing University Chongqing 400030 China Correspondence should be addressed to Z. M. Fang fangzhimiao1983@163.com Received 7 March 2010 Accepted 9 July 2010 Academic Editor Nikolaos Papageorgiou Copyright 2010 Z. M. Fang and S. J. Li. 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. This paper investigates the upper semicontinuity of the solution map for a parametric weak vector variational inequality associated to a c-hemicontinuous and weakly C-pseudomonotone operator. 1. Introduction and Preliminaries A vector variational inequality VVI in short was first introduced by Giannessi 1 in the setting of finite-dimensional Euclidean space. Later on it was studied and generalized to infinite-dimensional spaces. Existences of the solutions for VVI have been studied extensively in various versions see 2-6 and references therein. Stability of the solution map for VVI or vector equilibrium problems is an important topic in optimization theory. A great deal of papers have been denoted to study the semicontinuity and continuity of the solution maps see 7-18 and references therein. All results of the stability of the solution map for VVI in the literature are obtained based on continuity of the operator. It is well known that c-hemicontinuity is weaker than continuity. In this paper our aim is to investigate the upper semicontinuity of the solution map for a parametric weak vector variational inequality associated to a c-hemicontinuous and weakly C-pseudomonotone operator. Let X Y and W the spaces of parameters be .