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Báo cáo hóa học: " Research Article System of Generalized Implicit Vector Quasivariational Inequalities"

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 System of Generalized Implicit Vector Quasivariational Inequalities | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 36845 9 pages doi 10.1155 2007 36845 Research Article System of Generalized Implicit Vector Quasivariational Inequalities Jian-Wen Peng and Xiao-Ping Zheng Received 14 February 2007 Revised 21 June 2007 Accepted 5 October 2007 Recommended by Kok Lay Teo We will introduce a system of generalized implicit vector quasivariational inequalities in short SGIVQVI which generalizes and unifies the system of generalized implicit variational inequalities the system of generalized vector quasivariational-like inequalities the system of generalized vector variational inequalities the system of variational inequalities the generalized implicit vector quasivariational inequality as well as various extensions of the classic variational inequalities in the literature and we present some existence results of a solution for the SGIVQVI without any monotonicity conditions. Copyright 2007 J.-W. Peng andX.-P. Zheng. 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 The vector variational inequality in short VVI in a finite-dimensional Euclidean space has been introduced in 1 and applications have been given. Chen and Cheng 2 studied the VVI in infinite-dimensional space and applied it to vector optimization problem in short VOP . Since then many authors 3-11 have intensively studied the VVI on different assumptions in infinite-dimensional spaces. Lee etal. 12 13 Lin etal. 14 Konnov and Yao 15 Daniilidis and Hadjisavvas 16 Yang and Yao 17 and Oettli and Schlager 18 studied the generalized vector variational inequality and obtained some existence results. Chen and Li 19 and Lee et al. 20 introduced and studied the generalized vector quasivariational inequality and established some existence theorems. Ansari 21 22 and Ding