This paper deals with equilibrium problems in the setting of metric spaces with a continuous convex structure. We extend Fan’s 1984 KKM theorem to convex metric spaces in order to employ some weak coercivity conditions to establish existence results for suitable local Minty equilibrium problems, where the involved bifunctions are ϕ-quasimonotone. By an approach which is based on the concept of the strong ϕ-sign property for bifunctions, weobtain existence results for equilibrium problemswhich generalize some results in the literature.
