Common fixed point theorems for pairs of subcompatible maps.

By H. Bouhadjera, C. Godet-Thobie. 2008

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AbstractIn this paper, we introduce the new concepts of subcompatibility andsubsequential continuity which are respectively weaker than occasionallyweak compatibility and reciprocal continuity. With them, we establisha common fixed point theorem for four maps in a metric space whichimproves a recent result of Jungck and Rhoades [7]. Also we give an-other common fixed point theorem for two pairs of subcompatible mapsof Greguˇs type which extends results of the same authors, Djoudi andNisse [3], Pathak et al. [12] and others and we end our work by giving athird 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), weaklycompatible maps, occasionally weakly compatible maps, subcompatiblemaps, subsequentially continuous maps, coincidence point, common fixedpoint, Greguˇs type.2000 Mathematics Subject Classification: 47H10, 54H25. 1 Historical introduction and new definitions

Subfields: Geometry and Topology

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