Open Access

Levitin-Polyak Well-Posedness for Equilibrium Problems with Functional Constraints

Journal of Inequalities and Applications20072008:657329

https://doi.org/10.1155/2008/657329

Received: 8 November 2007

Accepted: 11 December 2007

Published: 24 December 2007

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Sichuan University
(2)
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation
(3)
Department of Mathematics and Statistics, Curtin University of Technology

Copyright

© Xian Jun Long et al. 2008

This article is published under license to BioMed Central Ltd. 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.