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In this paper, we extend the concept of best proximity point to 2-metric spaces and prove the existence of such points for contraction type non-self mappings in the setting of complete 2-metric spaces. Also, we presented an example to support our results.

Abstract. In the present research, an interesting common best proximity point theorem for pairs of non-self-mappings is presented. It satisfies a weakly contraction-like condition, thereby producing common optimal approximate solutions of certain simultaneous fixed point equations.