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New cone fixed point theorems for nonlinear multivalued maps with their applications. (English) Zbl 1218.54037

Summary: We first establish some new types of fixed point theorems for nonlinear multivalued maps in cone metric spaces. From those results, we obtain new fixed point theorems for nonlinear multivalued maps in metric spaces and the generalizations of Mizoguchi-Takahashi’s fixed point theorem and Berinde-Berinde’s fixed point theorem. Some applications to the study of metric fixed point theory are given.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E99 Topological spaces with richer structures
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