Generic uniqueness of equilibrium points Original Research Article

Let XX be a nonempty, convex and compact subset of normed linear space EE (respectively, let XX be a nonempty, bounded, closed and convex subset of Banach space EE and AA be a nonempty, convex and compact subset of XX) and f:X×X→Rf:X×X→R be a given function, the uniqueness of equilibrium point for equilibrium problem which is to find x∗∈Xx∗∈X (respectively, x∗∈Ax∗∈A) such that f(x∗,y)≥0f(x∗,y)≥0 for all y∈Xy∈X (respectively, f(x∗,y)≥0f(x∗,y)≥0 for all y∈Ay∈A) is studied with varying ff (respectively, with both varying ff and varying AA). The results show that most of equilibrium problems (in the sense of Baire category) have unique equilibrium point.