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We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying φ-contractive conditions or ψ-φ-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.

UNIQUE POINT OF COINCIDENCE FOR TWO MAPPINGS WITH 𝜑- OR 𝜓-𝜙-CONTRACTIVE CONDITIONS ON 2-METRIC SPACES