Uniqueness and Holder continuity of the solution to multivalued equilibrium problems in metric spaces

摘要

Multivalued equilibrium problems in general metric spaces are considered. Uniqueness and Holder continuity of the solution are established under Holder continuity and relaxed Holder-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 <.,.>.