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An order on subsets of cone metric spaces and fixed points of set-valued contractions. (English) Zbl 1187.47041
Summary: We introduce a new order on the subsets of cone metric spaces and, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.

MSC:
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:
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