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Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces. (English) Zbl 1156.90025

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:

90C47 Minimax problems in mathematical programming
90C31 Sensitivity, stability, parametric optimization
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