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In this paper we prove a coincidence point result in a space which does not have to satisfy any of the classical axioms that define a metric space. Furthermore, the ambient space need not be ordered and does not have to be complete. Then, this result may be applied in a wide range of different settings (metric spaces, quasi-metric spaces, pseudo-metric spaces, semi-metric spaces, pseudo-quasi-metric spaces, partial metric spaces, G-spaces, etc.). Finally, we illustrate how this result clarifies and improves some well-known, recent results on this topic.

Some fixed/coincidence point theorems under ( ψ , φ ) -contractivity conditions without an underlying metric structure