The main theorem extends Theorem K of the author’s paper in Boll. Unione Mat. Ital., N. Ser. A 4, 29-34 (1985). Theorem 1. Let \(T: X\to CB(X)\) and let \(f: X\to X\) and \(g: X\to X\) be continuous mappings for which T(X)\(\subseteq f(X)\cap g(X)\). Suppose that T commutes with f and g and that there exists \(h\in (0,1)\) such that \[ H(T(x),T(y))\leq hd(f(x),g(y)) \] for each x,y\(\in X\). Moreover, assume that one of the following holds: either (i) \(f(x)\neq f^ 2(x)\) implies \(f(x)\cap T(x)=\emptyset\) or (ii) \(g(x)\neq g^ 2(x)\) implies \(g(x)\cap T(x)=\emptyset\). Then T has a fixed point in X (which is also a fixed pont of f or g).