Abstract
Abstract In this note, we emphasize that the proofs and statements of the main results of the paper ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces’ (Journal of Inequalities and Applications 2013, 2013:210) do not have any utility to use the partial metric. Hence, it has no contribution to either partial metric theory or Caristi-type fixed point problems. MSC:47H10, 54H25.
Highlights
In this note, we emphasize that the proofs and statements of the main results of the paper ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces’ (Journal of Inequalities and Applications 2013, 2013:210) do not have any utility to use the partial metric
It is well known that (X, p) is complete if and only if (X, dp) is complete. Under these observations, keeping ( ) in mind, we conclude that Lemma . in [ ] remains true without using any properties of a partial metric
In Definition . in [ ], the open and closed balls associated to a partial metric p are not defined correctly, because the term p(x, x) is missing, that is, we should have
Summary
We emphasize that the proofs and statements of the main results of the paper ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces’ (Journal of Inequalities and Applications 2013, 2013:210) do not have any utility to use the partial metric. We use the same definitions, notations and structures given in [ ]. We start first with Caristi’s [ ] fixed point theorem. [ ] Let (X, d) be a complete metric space.
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