Journal of Inequalities and Applications 
Volume 2008 (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

 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

Recommended by Simeon Reich

Abstract

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.