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A common fixed point theorem for a class of mappings. (English) Zbl 0533.54031

The authors have proved the following theorem.

Theorem. Let A be a selfmapping of X, and S and T be continuous selfmappings on X satisfying the following conditions: (I) {A,S} and {A,T} are weakly commuting pairs such that A(X)S(X)T(X); (II) there exists a φΨ such that for all x,yX


where φ satisfies (III) for any t>0, φ(t,t,a 1 t,a 2 t,t)<t, where a 1 +a 2 =3· Then A, S and T have a unique common fixed point in X.

Reviewer: J.Achari

54H25Fixed-point and coincidence theorems in topological spaces