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Discontinuity and fixed points. (English) Zbl 0938.54040
The author gives a fixed point theorem for a self-map of a metric space \((X,d)\) under a contractivity condition which does not force the map to be continuous at the fixed point. He also gives a common fixed point theorem for two self-mappings \(f,g\) which satisfy a contractivity condition and moreover are “weakly commuting”, i.e. there exists some positive real number \(R\) such that \(d(ffx, gfx)\leq R\cdot d(fx,gx)\).
Reviewer: D.Roux (Milano)

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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