Common fixed point theorem for occasionally weakly compatible maps satisfying a contractive condition with altering distance
DOI:
https://doi.org/10.37135/ns.01.10.02Keywords:
Common fixed point, commutativity, occasionally weakly compatible map, altering distance function, E. A. propertyAbstract
This paper aims to establish conditions that guarantee the existence and uniqueness of a common fixed point for a pair of functions defined on a metric space, satisfying a type of contractive inequality involving distance-altering functions. We use some weaker forms of commuting maps to achieve our results, concretely, occasionally weakly compatible maps. We prove that if are occasionally weakly compatible maps with a coincident point such that where and is an altering distance function, then and have a unique common fixed point. This result generalizes some theorems of common fixed points where neither the continuity of maps nor the completeness of the metric space is required.
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References
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