Applied Mathematics & Information Sciences

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In this paper, we extend the concept of generalized proximal contractions of the first kind to proximal (a,b )y -contractions types A and B. We show with examples that our new classes of mappings is real generalization of many known classes of non-self and self mappings in literature. We also introduce some condition for proving the best proximity point theorems in such classes. Applying our new concepts, we obtain best proximity point results on metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph.

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