Fixed points of multivalued nonexpansive maps. (English) Zbl 0667.47028

Husain, Taqdir; Latif, Abdul

Math. Jap. 33, No. 3, 385-391 (1988).

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:

47H10	Fixed-point theorems
54C60	Set-valued maps in general topology
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

existence of fixed points for non-expansive correspondences; Opial’s condition

Citations:

Zbl 0179.199