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In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN ; 2) Tm,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

Uniqueness of Common Fixed Points for a Family of Mappings with &lt;i&gt;Φ&lt;/i&gt;-Contractive Condition in 2-Metric Spaces

Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces