Sentence examples for result will be established from inspiring English sources

The convergence result will be established as following.

The proof of our result will be established through several lemmas.

Indeed, our result will be established under the conditions g'(t) ≤ 0 and ∫ 0 ∞ ξ ( s ) g ( s ) d s < ∞ for some nonnegative function ξ(t).

Our results will be established below under the hypothesis.

In contrast to the techniques of proving in [1], our results will be established by virtue of the famous Hardy inequality.

Weak convergence result under mild assumptions will be established.

Strong convergence results of these methods will be established under very mild conditions.

In Section 3, the existence and uniqueness result for the solution to problem (1.1) will be established with the help of the contraction mapping principle.

Meanwhile, the Newton-SOR iterative method will be proposed under these conditions for numerically solving such a positive eigenvector, and some convergence results on this iterative method will be established for the nonlinear eigenvalue problems with an irreducible singular M-matrix, a nonsingular M-matrix, and a general M-matrix, respectively.

To make the results publicly accessible, a database will be established.

A comprehensive master database using Citation Manager 10.0 software will be established incorporating results of all searches.