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On fixed point theorems for absolute retracts. (English) Zbl 0994.47053
In the paper under review a Schauder type fixed point theorem is proved. The assumption of compactness of the mapping is replaced by a much weaker condition. As a corollary a generalization of the Darbo-Sadovski fixed point theorem for \(\alpha _E\)-nonexpansive mappings is obtained (\(\alpha _E\) denotes the Kuratowski measure of noncompactness). The results are illustrated by suitable examples and compared with some known results. The paper is concluded by some open problems.

MSC:
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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