Variational relation problems in locally convex spaces

Let A,B and Y be nonempty sets, S1 : A⇒ A, S2 : A ⇒ B, B : B × B ⇒ Y be set-valued mappings with nonempty values and R(a, b, y) be a relation linking elements a ε B, b ε B and y ε Y . In [1] Luc established existence theorems for solutions of the following problem: find ā ε B such that ā is a fixed point of S1 and R(ā, b, y) holds for all b ε S2(ā) and y ε B(ā, b). In this paper the same problem is investigated in locally convex Hausdorff topological vector spaces. Significant particular cases (quasivariational inclusion problems, quasivariational intersection problems, quasioptimization problems) will be also discussed.