COMMON FIXED POINT THEOREMS FOR PAIRS OF SUBCOMPATIBLE MAPS

Abstract

In this paper, we introduce the new concepts of subcompatibility and subsequential continuity which are respectively weaker than occasionally weak compatibility and reciprocal continuity. With them, we establish a common fixed point theorem for four maps in a metric space which improves a recent result of Jungck and Rhoades [7]. Also we give another common fixed point theorem for two pairs of subcompatible maps of Greguˇs type which extends results of the same authors, Djoudi and Nisse [3], Pathak et al. [12] and others and we end our work by giving a third result which generalizes results of Mbarki [8] and others. Key words and phrases: Commuting and weakly commuting maps, compatible and compatible maps of type (A), (B), (C) and (P), weakly compatible maps, occasionally weakly compatible maps, subcompatible maps, subsequentially continuous maps, coincidence point, common fixed point, Greguˇs type