have studied coincidences and fixed points of nonself hybrid contractions on metrically convex spaces. However, most of their main theorems contain errors and admit counterexamples. In this paper, we rectify these results and obtain coincidence and fixed point theorems on a more general setting.

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It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.