Sentence examples for proved by the same method from inspiring English sources

The other inequalities in (4.4) can be proved by the same method.

The assertion (iv) is proved by the same method used in (ii).

The following result can be proved by the same method as Corollary 3.7 of [5].

We summary the basic properties of { x t }, which can be proved by the same method in [18].

The truth of (6) is based upon the following lemma, which can be proved by the same method as the proof of Lemma 4 [33].

We end this section with the following Rellich-type inequality on the polarizable group which can be proved by the same method if we noted Theorem and Proposition in [21] and the weighted Hardy inequality (Theorem ) in [22].

Conclusion (3) in Theorem 3.5 can be proved by using the same method as in [8].

Proof The assertion in part (i) of Theorem 2 can be proved by using the same method as in the proof of Theorem 1, part (i), above.

Recently, Vijayaraju [21] proved by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces.

If (tau>tau_{2}^{h_{1}}), then the result can be proved by using the same methods as those for case (SC11).

The third inequality can be proved by the same argument.