2-度量空间上φ_j-拟收缩型映射族的公共不动点的唯一性

Uniqueness of Common Fixed Points for a Family of Maps with φ_j-Quasi-Contractive Type in 2-Metric Spaces

引进了5元函数类Φ,构造了满足一种φ_j-拟收缩型条件的2-度量空间(X,d)上的自映射族{T_(i,j)}_i∈N∪{0},j∈N决定的收敛序列,然后证明了当X是完备且满足条件T_(a,μ)·T_(β,v)=T_(β,v)·T(a,μ),(?)α,β∈N∪{0},μ,v∈N且μ≠v时,该序列的极限就是该映射族{T_(i,j)}_i∈N∪{0},j∈N的唯一的公共不动点.该文的定理推广和改进了很多2-度量空间上的唯一公共不动点定理.

A class of 5-dimensional functions $ was introduced,and a convergent sequencedetermined by a family of self-maps {T_（i,j）}_（i∈N∪{0},j∈N）,which satisfy someφ_j-contractive conditionin a 2-metric space,was constructed,and then that the limit of the sequence is the uniquecommon fixed point of the maps {T_（i,j）}_（i∈N∪{0},j∈N） was proved when X is complete and thefollowing condition T_（α,μ） ？ T_（β,ν） = T_（β,ν）·T_（α,μ） for allα,β∈N∪{0},μ,ν∈N,μ≠νis satisfied.Our main theorem improves and generalizes many known unique common fixed point theoremsin 2-metric spaces.