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Abstract In this paper, we give some necessary and sufficient conditions under which the topology generated by a partial metric is equivalent to the topology generated by a suitably defined… Click to show full abstract
Abstract In this paper, we give some necessary and sufficient conditions under which the topology generated by a partial metric is equivalent to the topology generated by a suitably defined metric. Next, we study some new extensions of the Generalized Banach Contraction Principle to partial metric spaces. Moreover, we draw a particular attention to the space of all sequences showing, in particular, that some well-known fixed point theorems for ultrametric spaces, can be used for operators acting in that space. We illustrate our considerations by suitable examples and counterexamples.
Journal Title: Mathematica Slovaca
Year Published: 2020
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