Sentence examples for using the Korovkin approximation from inspiring English sources

We study approximating properties of these operators using the Korovkin approximation theorem and also study a direct theorem.

Also, we investigate the statistical approximation properties of the q-Kantorovich-Stancu operators using the Korovkin-type statistical approximation theorem.

Proof By using the Korovkin theorem in [12], we see that it is sufficient to verify the following three conditions.

Using the Korovkin-type theorem on weighted approximations in [25], we see that it is sufficient to verify the following three conditions: lim_{nrightarrowinfty} biglVert K_{n,q_{n}} bigl(e_{i}(t);x bigr -e_{i}(x) bigr -e_{i}rho}=0,quad i=0,1,2.

Now, combining (3.5 - 3.7 3.5 - 3.7ng the standstical version of the Korovkin approximation theorem (see Gadjiv and Orhan [10], Theorem 1), we get the desired resusing

In this paper, we use the notion of statistical summability ( C, 1 ) to prove the Korovkin approximation theorem for the functions 1, cos and sin in the space of all continuous 2π-periodic functions on the real line and show that our result is stronger.

obtained using the Euler approximation as (14).

The FMT data were reconstructed using the normalised Born approximation using the slab approximation [ 27].

The dipole approximation is developed using the approximation of a flat semi-infinite medium.

Exchange correlation was described using the generalized gradient approximation in the Perdew–Burke Ernzerhof implementation.

The exact numerical solution can then be graphically compared to the solution using the approximation.