Sentence examples for using this lemma we from inspiring English sources

Using this lemma, we could establish our blowup rate estimate.

Using this lemma, we generalize the identities considered in the previous two sections.

Using this lemma, we have a similar conclusion to Theorem 3.1 with less stringent assumptions.

Using this lemma, we prove the main result of this section.

Using this lemma, we can show that the map (vartheta colon Clongrightarrow C) defined earlier is compact.

Using this lemma, we prove some fixed point and common fixed point results for -weakly contractive mappings in the setup of ordered partial b-metric spaces.

Using this Lemma 2.1, we can prove that the set of fixed points of is closed and convex.

Using this lemma along with the semigroup property, we now show that the limiting operators exist and are well-defined.

Using this lemma together with (2.1) and (2.2), we have the following bilateral growth restrictions on the primitive G.

Now we use this lemma to prove our theorems.

We use this lemma in the proof of our necessary efficiency result.