In this paper, we establish sufficient conditions for the existence of solutions of equilibrium problems in a metric space, that do not involve any convexity assumption either for the domain or for the function. To prove these results, a weak notion of semicontinuity is considered. Furthermore, some existence results for systems of equilibrium problems are provided.

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...

Flesch et al [3] showed that, if the payoff functions are bounded and lower semicontinuous, then such a game always has a pure, subgame perfect -equilibrium for > 0. Here we prove the same result for bounded, upper semicontinuous payoffs. Moreover, Example 3 in Solan and Vieille [7] shows that if one player has a lower semicontinuous payoff and another player has an upper semicontinuous payoff,...

We introduce the concept of fuzzy co-r-M -semicontinuous, and investigate the relationships between fuzzy co-r-M -semicontinuous mappings and several types of fuzzy r-minimal semicompactness.