Inclusion and intersection theorems with applications in equilibrium theory in g-convex spaces
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Balaj, Mircea; O'Regan, Donal (2010). Inclusion and intersection theorems with applications in equilibrium theory in g-convex spaces. Journal of the Korean Mathematical Society 47 (5), 1017-1029
In this paper we obtain a very general theorem of rho-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 rho on 2(Z) and three mappings P : X (sic) Z, Q : Y (sic) Z and T is an element of B(Y, X) satisfying a set of conditions we can find ((x) over tilde, (y) over tilde) is an element of X x Y such that (x) over tilde is an element of T((y) over tilde) and P((x) over tilde)rho Q((y) over tilde). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.