(ε, δ) contractive condition and common fixed points
2009
scientific article
english
- common fixed point
- compatible maps
- noncompatible maps
- weak compatible maps of type (A)
- contractive condition and reciprocal continuity
EN In the present paper we prove a common fixed point theorem (Theorem 1) for four mappings under the (ε, δ) contractive condition, however, without either imposing any additional restriction on δ or assuming the Φ-contractive condition together with. While proving the theorem, neither the completeness of the metric space is assumed nor any of the mappings is required to be continuous. Thus we also provide one more answer to the problem of Rhoades [24] which ensures the existence of common fixed point, however, does not force the maps to be continuous at the common fixed point. Theorem 2 generalizes further the result obtained in Theorem 1.
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CC BY-NC-ND (attribution - noncommercial - no derivatives)
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