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Be careful on partial metric fixed point results. (English) Zbl 1267.54044

Let \((X,p)\) be a partial metric space. Then the functional \(d: X \times X \to \mathbb R_+\) defined by \(d(x,y) = 0\) whenever \(x = y\) and \(d(x,y) = p(x,y) \) whenever \(x \neq y\), is a metric on \(X\). In this paper the authors show that some fixed point generalization to \((X,p)\) can be obtained from the corresponding results in \((X,d)\).

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54E99 Topological spaces with richer structures
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