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Zbl 1156.90025
Anh, Lam Quoc; Khanh, Phan Quoc
(Lam Quoc Anh; Phan Quoc Khanh)
Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces.
(English)
[J] J. Glob. Optim. 37, No. 3, 449-465 (2007). ISSN 0925-5001; ISSN 1573-2916/e

Summary: Multivalued equilibrium problems in general metric spaces are considered. Uniqueness and Hölder continuity of the solution are established under Hölder continuity and relaxed Hölder-related monotonicity assumptions. The assumptions appear to be weaker and the inclusion to be properly stronger than that of the recent results in the literature. Furthermore, our theorems include completely some known results for variational inequalities in Hilbert spaces, which were demonstrated via geometrical techniques based on the orthogonal projection in Hilbert spaces and the linearity of the canonical pair $\langle .,.\rangle$.
MSC 2000:
*90C47 Minimax problems
90C31 Sensitivity, etc.

Keywords: Metric spaces; Multivalued equilibrium problems; Hölder properties; Variational inequalities; Fixed point and coincidence point problems; Vector optimization

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