Altman’s contractors and fixed points of multivalued mappings

Let Pt: D⊂X1 × … × Xn → CL (Yi) be multivalued mappings where Xi Yi are Banach spaces and CL (Yi) is the set of all nonempty closed subsets of Yi i=1,…, n. We prove a theorem ensuring that θ ∈ Pi(x1…xn) for some (x1…xn) ∈ D and deduce the fixed point theorems for multivalued mappings proved earlier by Czerwik, Nadler and Reich as corollaries.Besides, generalizations for multivalued mappings of the existence theorems proved by Altman using his theory of contractors are also obtained. © 1982, University of California, Berkeley. All Rights Reserved.