Discontinuity and fixed points
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 \(d(ffx, gfx)\leq R\cdot d(fx,gx)\).
scientific article; zbMATH DE number 1398609