Set-Valued Robust Mappings and Approximatable Mappings

Weighted Variational Inequalities with Set-valued Mappings

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...

A Sard Theorem for Set-Valued Mappings∗†

If F is a set-valued mapping from IRn into IRm with closed graph, then y ∈ IRm is a critical value of F if for some x with y ∈ F (x), F is not metrically regular at (x, y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m − 1 (resp. a ...

Fixed Point Theorems for Set-valued Mappings

On Common Fixed Points of Weakly Commuting Mappings and Set - Valued Mappings

ABS]RACT. Our main theorem establishes the uniqueness of the common fixed point of tw set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author. Let (X,d) be a complete metric space and let B(X) be the set of all nonempty, bounded subsets of X As in [I], l...

Σ-products and selections of set-valued mappings

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.