  We consider scalar equilibrium problems governed by a bifunction in a
finite-dimensional framework. By using classical arguments in Convex Analysis,
we show that under suitable generalized convexity assumptions imposed on the
bifunction, the solutions of the equilibrium problem can be characterized by
means of extreme or exposed points of the feasible domain. Our results are
relevant for different particular instances, such as variational inequalities
and optimization problems, especially for best approximation problems.
