Sentence examples for as regards the operator from inspiring English sources

The purpose of this paper is to propose a simultaneous iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information as regards the operator norms.

The advantage of our choice (1.7) of the stepsizes lies in the fact that no prior information as regards the operator norms of A and B is required, and still convergence is guaranteed.

To estimate the norm of an operator is not always easy, and if it is not easy to estimate the norm of an operator, we purpose another iterative algorithm with a way of selecting the step-sizes such that the implementation of the algorithm does not need any prior information as regards the operator norm.

Recently, in order to solve the problem (1.8), Moudafi and Thakur [18] presented the following split proximal algorithm with a way of selecting the step sizes such that its implementation does not need any prior information as regards the operator norm.

In Section 3, we prove the generalized Hardy-Knopp type inequalities as regards the operator (T^{r}_{k}) and derive the corresponding conclusions in a multidimensional form.

Here, without the Lipschitz assumption of f, we make full use of the technique of the compactness as regards the solution operator to obtain the solvability of the controlled nonlocal impulsive equation (3.1).

We also refer to [6] for more information as regards the resolvent or solution operator.

For more information as regards the properties of Dirac operators and left monogenic functions can be found in [2, 3, 27 29].

As regards the provisions for data transfers for commercial purposes, operators should not have to constantly change compliance models.

For example, in [20], Tomita regarded the operator (I_{alpha}) as a special case of pseudo-differential operator and proved the following results.

However, this registry contains limited information regarding the operator.