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In this paper, we present some new generalizations of Mizoguchi-Takahashi’s fixed point theorem which also improve and extend Du-Hung’s fixed point theorem. Some new examples illustrating our results are also given. By applying our new results, some new fixed point theorems for essential distances and e0-metrics were established.

New Generalized Mizoguchi-Takahashi’s Fixed Point Theorems for Essential Distances and e0-Metrics