TITLE:
Uniqueness of Common Fixed Points for a Family of Mappings with Φ-Contractive Condition in 2-Metric Spaces
AUTHORS:
Yong-Jie Piao
KEYWORDS:
2-Metric Space; 5-Dimensional Functions Φ ;Φ-Contractive Condition; Cauchy Sequence; Common Fixed Point
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.1,
January
4,
2012
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.