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A note on the equivalence of some metric and cone metric fixed point results. (English) Zbl 1213.54067

Let E be a Hausdorff topological vector space and K be a proper closed convex cone of it, with nonempty interior. The following is the main result of the paper:

Theorem. Let (X,d) be a K-metric space. Take eint(K) and let q e be the Minkowski functional of [-e·e]. Then i) d q :=q e d is a standard metric on X, ii) d(x 1 ,y 1 )d(x 2 ,y 2 ) d q (x 1 ,y 1 )d q (x 2 ,y 2 ). As a consequence, most of the fixed point results for K-metric spaces are deductible from their standard versions (K= + ).


MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54E40Special maps on metric spaces
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