Unique common fixed point of a family of self-maps with same type contractive condition in 2-metric space

Abstract

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.