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On fixed points of \(\alpha\)-\(\psi\)-contractive multivalued mappings in cone metric spaces. (English) Zbl 1294.54029

Summary: We define the notion of \(\alpha^\ast\)-\(\psi\)-contractive mappings for cone metric spaces and obtain fixed points of multivalued mappings in connection with Hausdorff distance functions for closed bounded subsets of cone metric spaces. We obtain some recent results of the literature as corollaries of our main theorem. Moreover, a nontrivial example of an \(\alpha^\ast\)-\(\psi\)-contractive mapping satisfying all conditions of our main result is constructed.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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