Inclusion and intersection theorems with applications in equilibrium theory in G-convex spaces

In this paper we obtain a very general theorem of ρ-compatibility for three multivalued mappings, one of them from the class B. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation ρ on 2^Z and three mappings P: X {multimap} Z, Q: Y {multimap} Z and T ∈ B(Y,X) satisfying a set of conditions we can find (x~, y~) ∈ X ×Y such that x~ ⊂ T(y~) and P(x~) ρ Q(y~). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.