Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 657329, 14 pages
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

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu 610500, China
3Department of Mathematics and Statistics, Curtin University of Technology, Perth W.A. 6102, Australia

Received 8 November 2007; Accepted 11 December 2007

Academic Editor: Simeon Reich

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.


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.