Sentence examples for by using the argument from inspiring English sources

by using the argument used to prove (6.26).

Proof The proof can be easily obtained by using the argument in the proof of ([36], Theorem 3.1).

Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.

By using the argument in the proof of Theorem 3.4, we can also obtain the following result that is an extension of [[4], Theorem 3.8].

By using the argument in Section 3 together with the results in [25, 36, 40, 41], we can also obtain the analogous results for CAT 0) spaces.

By using the argument as above, we obtain x 3 ∈ T x 2 such that d ( x 2, x 3 ) < ( 1 + ϵ ( x 2 ) ) d ( x 2, T x 2 ).

Moreover, by using the arguments in the proof of Lemma 2.3, we have I ′ ( v 0 ) = 0 and I ( v 0 ) ∈ [ c − δ, c + δ ].

By using the arguments similar to that of the proof of Case (i) of Theorem 1.2 we can show that any solution u ( x, t ) of Problem (1.1) vanishes in finite time.

By using the same argument, we can prove that (3.84).

By using the above argument, we conclude that (3.33).

The (L^{2}_{omega^{(alpha,mu)}} -projection error (59) can be obtained by using the same argument.