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Báo cáo hóa học: " Research Article Levitin-Polyak Well-Posedness for Equilibrium Problems with Functional Constraints"

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 Levitin-Polyak Well-Posedness for Equilibrium Problems with Functional Constraints | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 657329 14 pages doi 10.1155 2008 657329 Research Article Levitin-Polyak Well-Posedness for Equilibrium Problems with Functional Constraints Xian Jun Long 1 Nan-Jing Huang 1 2 and Kok Lay Teo3 1 Department of Mathematics Sichuan University Chengdu Sichuan 610064 China 2 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Chengdu 610500 China 3 Department of Mathematics and Statistics Curtin University of Technology Perth W.A. 6102 Australia Correspondence should be addressed to Nan-Jing Huang nanjinghuang@hotmail.com Received 8 November 2007 Accepted 11 December 2007 Recommended by Simeon Reich We generalize the notions of Levitin-Polyak well-posedness to an equilibrium problem with both abstract and functional constraints. We introduce several types of generalized Levitin-Polyak well-posedness. Some metric characterizations and sufficient conditions for these types of well-posedness are obtained. Some relations among these types of well-posedness are also established under some suitable conditions. Copyright 2008 Xian Jun Long 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 Equilibrium problem was first introduced by Blum and Oettli 1 which includes optimization problems fixed point problems variational inequality problems and complementarity problems as special cases. In the past ten years equilibrium problem has been extensively studied and generalized see e.g. 2 3 . It is well known that the well-posedness is very important for both optimization theory and numerical methods of optimization problems which guarantees that for approximating solution sequences there is a subsequence which converges to a solution. The well-posedness of unconstrained and constrained scalar