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Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces
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Abstract
In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {T i,j } iεN in 2-metric space have an unique common fixed point if 1) {T i,j } iεN satisfies Φ j -contractive condition, where Φ j εΦ, for each jεN ; 2) T m,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.
Keywords2-Metric Space5-Dimensional Functions Φ<i>Φ</i>-Contractive ConditionCauchy SequenceCommon Fixed Point
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