Uniqueness of Common Fixed Points for a Family of Mappings with Φ-Contractive Condition in 2-Metric Spaces ()
Abstract
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.
Share and Cite:
Y. Piao, "Uniqueness of Common Fixed Points for a Family of Mappings with
Φ-Contractive Condition in 2-Metric Spaces,"
Applied Mathematics, Vol. 3 No. 1, 2012, pp. 73-77. doi:
10.4236/am.2012.31012.
Conflicts of Interest
The authors declare no conflicts of interest.
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