Common fixed points of conditionally commuting maps

In the instant paper, redefining the concept of occasionally weakly compatible mappings, given by Jungck and Rhoades [3], we introduce the notion of conditionally commuting mappings. We first prove a common fixed point theorem (Theorem 1) for a pair of noncompatible mappings without assuming completeness of the space or continuity of the mappings involved. This theorem extends the result of Pant [7]. In Theorem 2, we further generalize the result obtained in Theorem 1. For this purpose we use the property (E.A) given by Aamri and Moutawakil [1].