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Abstract. In this paper
we give sufficient conditions for the existence of solutions of Problem (P1) (resp.
Problem (P2))
of finding a point (z0, x0)\in B(z0, x0) × A(x0)
such that F(z0, x0, x) ⊂ C(z0, x0, x0) (resp. F(z0, x0, x0) ⊂ C(z0, x0, x)) for
all x ∈ A(x0), where A,
B, C, F are set-valued maps between locally convex Hausdorff
spaces. Some known existence theorems are included as special cases of the
main results of the paper.
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