Sentence examples for by using the completeness from inspiring English sources

By using the completeness of X, there exists (x^in X) such that (x_{n}rightarrow x^) as (nrightarrowinfty).

It can be shown that the weighted Orlicz space is also a Banach space by using the completeness of the usual Orlicz space.

By using the completeness earthquake dataset, the calculated values of b and D C were found to imply variations in seismotectonic stress.

By using the completeness result of Lemma 8 and the orthogonality relation of Lemma 9, we can easily prove the uniqueness result.

Using the completeness of (L^{p}_{mathrm{loc}}(mathbb{R}, X)), we denote by (y(t)) the pointwise limit of (y_{i}(t)).

Completeness of follow-up was calculated using the completeness index.

By using the new type of completeness, we establish some common fixed point theorems for two self-mappings satisfying a nonlinear contractive condition of Ćirić type.

By using the new type of completeness, we establish some common fixed point results on dislocated quasi-metric spaces, which generalize and unify the results of Ume [5], Ilić and Rakočević [6], Di Bari and Vetro [7], He [8], Amini-Harandi [17], Shukla et al. [18] and some others.

The purpose of this work is to weaken the condition of completeness of the metric space in the result of Kutbi and Sintunavarat [5] by using the concept of α-completeness of the metric space.

The completeness is calculated by using the following Equation 12.

7 We assessed the completeness of the Obstetric Database by using the National Patient Register as a gold standard.