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On coincidence point and fixed point theorems for nonlinear multivalued maps. (English) Zbl 1231.54021

Summary: Several characterizations of \(\mathcal{MT}\)-functions are first given in this paper. Applying the characterizations of \(\mathcal{MT}\)-functions, we establish some existence theorems for coincidence points and fixed points in complete metric spaces. From these results, we can obtain new generalizations of Berinde-Berinde’s fixed point theorem and Mizoguchi-Takahashi’s fixed point theorem for nonlinear multivalued contractive maps. Our results generalize and improve some main results in the literature.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
54E50 Complete metric spaces
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