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Coincidences and fixed points of reciprocally continuous and compatible hybrid maps. (English) Zbl 1011.47042

Summary: 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.

MSC:

47H10 Fixed-point theorems
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