UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if (i) {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; (ii) Tm,μ· Tn,ν = Tn,ν· Tm,μ for all m,n,μ,ν∈ N with μ = ν. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.