Sentence examples for an alternative proof of from inspiring English sources

Moreover, we give an alternative proof of the Brezis-Gallouet-Wainger inequality.

We also obtain an alternative proof of stability results concerning Yu's property A.

This paper also contains other theorems including an alternative proof of Davydov and Tombak's result.

In this paper, we derive an alternative proof of the sufficient condition using special properties of βk.

This result, together with the approximate configurations constructed by C. Taubes (Comm. Math. Phys. 80, 1981, 343-367), yields an alternative proof of the existence of such solutions.

In the case of a symmetric recurrence a ready consequence of that correspondence is an alternative proof of Favard's Theorem and the Representation Theorem.

In order to obtain estimates of the Sobolev orthogonal polynomials (hat{B}_n) we follow, essentially, the same techniques used in these papers and we present an alternative proof for a special case of [11, Theorem 4] (see the proof of Theorem 1) based on the connection formulas.

Particularly, we give an alternative proof to show that the space of Stepanov-like weighted pseudo almost periodic functions is a Banach space.

Certain results of this paper can be applied to give an alternative proof and generalization of the optimal form of the limiting case of the Sobolev embedding theorem due to Hansson and Brezis Wainger.

Therefore, we do not follow this way and give a simple alternative proof of a related assertion for discrete time scales.

This is an alternative proof and an extension of a result in Chen et al. [13].