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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)
##### Keywords:
contractivity condition
Full Text:
##### References:
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