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

Yong-Jie Piao

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DOI: 10.4236/am.2012.31012                

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_jεΦ, 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.

Keywords

2-Metric Space; 5-Dimensional Functions Φ ;Φ-Contractive Condition; Cauchy Sequence; Common Fixed Point

Conflicts of Interest

The authors declare no conflicts of interest.

References

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