On a Common Fixed Point Problem for Two Pairs of Maps Satisfying the Property (W.T)

Abstract

We introduce a new property that we call the property (W.T). This property generalizes and unifies the concept of noncompatible mappings due to Jungck (1986), the property (E.A) of Aamri and Moutawakil (2002) and the concept of asymptotically regular maps due to Browder and Petryshyn (1966). We use this concept to prove a general common fixed point for two pairs of compatible maps under a contractive condition of Lipschitz type. We study also the well-posedness of the fixed point problem for these maps. Our main result extends, unifies and improves several recent results involving this Lipschitz type condition which is is not a contractive condition of the classical type. So our work provides some new contributions to the field of metric fixed point theory.