Sentence examples for provides the uniqueness from inspiring English sources

The following condition provides the uniqueness of fixed points of the maps considered in Theorem 2.3 and Theorem 2.4.

Theorem 8 asserts that assumption (u0) together with Corollary 2 provides the uniqueness of common fixed point.

In this section, we provide the uniqueness and conditional stability in Theorems 3.1 and 3.2, respectively.

This self-organization is believed to provide the uniqueness required in designing 3D cell orientation architecture for reconstructed muscle tissue.

In the following example we show that Theorem 1 does not provide the uniqueness of the fixed point in general.

As condition (1) was derived for infinite planar layer, in the modeling of the wave-scattering by finite surfaces it must be combined with the edge condition to provide the uniqueness of the BVP solution.

It also provides the first uniqueness result for a Fitzhugh Nagumo system.

Consequently, Theorem 2.3 provides the existence and uniqueness of the fixed point of f. □.

(17) Then the existence of a lower solution or an upper solution of problem (16) provides the existence and uniqueness of a solution of problem (16).

(2.10) An abstract Galerkin method provides the existence and uniqueness result for the solution of problem (2.10) for any (varepsilon >0) and also some a priori estimates (see [5]).

And then, we provide the existence, uniqueness, stability, and convergence for its CSM solutions.