The author studies the approachability of multifunctions by single-valued continuous functions and its applications to fixed point and coincidence theory. He outlines stability features of this property relevant to fixed point theory, and he provides examples of non-convex and non-contractible approachable multifunctions. He also presents a simple and straightforward treatment of the fixed point and coincidence properties for such multifunctions defined on non-compact subsets of topological vector spaces and essentially generalizes the Himmelberg fixed point theorem to broad classes of non-convex multifunctions. The results presented here find applications in the theory of variational inequalities and complementarity problems as well as in game theory.
For the entire collection see [Zbl 0836.00031].