A common fixed point theorem for a class of mappings
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 \(A(X)\subset S(X)\cap T(X);\) (II) there exists a \(\phi\in\Psi\) such that for all \(x,y\in X\) \[ d(Ax,Ay) \leq \phi(d(Sx,Ty), d(Sx,Ax), d(Sx,Ay), d(Ty,Ax), d(Ty,Ay)) \] where \(\phi\) satisfies (III) for any \(t>0\), \(\phi(t,t,a_ 1t,a_ 2t,t)<t,\) where \(a_ 1+a_ 2=3.\) Then A, S and T have a unique common fixed point in X.
scientific article; zbMATH DE number 3846457