Sentence examples for using the partial metric from inspiring English sources

The proof of the following lemma can be easily done by using the partial metric topology.

Remark 3.2 Even though the results of Haghi et al. can deduce the same fixed point as the corresponding partial metric fixed point result, using the partial metric version computers evaluate faster since many nonsense terms are omitted.

Remark 4.3 It should be pointed out, however, that even though the results of Haghi et al. can deduce the same fixed point as the corresponding partial metric fixed point result, using the partial metric version computers evaluate faster since many nonsense terms are omitted.

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.

Recently Haydi et al. introduced a partial Hausdorff metric on a partial metric space and they extended Nadler's fixed point theorem on partial metric spaces using the partial Hausdorff metric.

Consequently, we derive Theorem 3.5 in [1] without using any property of the partial metric.

We use the abbreviation PMS for the partial metric space (X, p).

It consists of separating the partial metric into two metrics: the channel metric and the a priori metric.

At this point, it seems natural to wonder if another choice of the partial metric couldallow to use Matthews fixed-point theorem for the purpose of discussing running time ofcomputing in asymptotic complexity analysis of algorithms.

The next result reveals the reason for which the partial metric spaces can be used as a suitable mathematical tool to describe Scott processes (see [3] for a deeper discussion).

Later, the authors in [17] proved a more reasonable contraction principle in the partial metric space in which they used self-distance terms.