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On the Equivalence of the Mizoguchi-Takahashi Locally Contractive Map and the Nadler’s Locally Contractive Map

Abstract In this paper, the equivalence between multi-valued maps satisfying the Mizoguchi-Takahashi’s uniformly locally contractive condition and multi-valued maps satisfying the Nadler’s uniformly locally contractive condition is obtained on metrically convex space. We have provided examples to illustrate that this equivalence need not be true on any arbitrary metric space.