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A new class of nonexpansive type mappings and fixed points. (English) Zbl 1003.54024
Summary: A new class of self-mappings on metric spaces which satisfy a nonexpansive type condition is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem which is converse to the Banach contraction principle is given.

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