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Zbl 1218.54037
Du, Wei-Shih
New cone fixed point theorems for nonlinear multivalued maps with their applications. (English)
[J] Appl. Math. Lett. 24, No. 2, 172-178 (2011). ISSN 0893-9659

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 2000:: *54H25 Fixed-point theorems in topological spaces
54E99 Topological spaces with richer structures

Keywords: $TVS$-cone metric space; Nadler's fixed point theorem; Mizoguchi-Takahashi's fixed point theorem; Berinde-Berinde's fixed point theorem

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Zentralblatt MATH Berlin [Germany]