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Fixed points of multivalued nonexpansive maps. (English) Zbl 0667.47028
The authors prove two theorems on the existence of fixed points for non- expansive correspondences. Here ‘non-expansive’ is not the usual notion related to the Hausdorff metric but to other definitions more “single- valued” in nature. The theorems are closely allied to theorems for non- expansive mappings in that they require the ambient space to satisfy Opial’s condition [Z. Opial, Bull. Am. Math. Soc. 73, 591-597 (1967; Zbl 0179.199)].
Reviewer: A.C.Thompson

MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
54C60Set-valued maps (general topology)
47H09Mappings defined by “shrinking” properties