A class of 5-dimensional functions Φ was introduced, and a convergent sequence determined by a family of self-maps {Ti, j }i∈N∪{0}, ~j∈N,
which satisfy some Φj-contractive condition in a 2-metric space, was constructed, and then that the limit of the sequence is the unique common fixed point of the maps {Ti, j }i∈N∪{0}, j∈N was proved when X is complete and the following condition Tα, μ ? Tβ, ν=Tβ, ν? Tα, μ , ∨α, β ∈N∪{0}, μ, ν ∈N, μ≠ν, is satisfied. Our main theorem improves and generalizes many known unique common fixed point theorems in 2-metric spaces.
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