Sentence examples for operator by using the from inspiring English sources

So you can get the function of the OR operator by typing in the "any of these words" box, for instance, or the NOT operator by using the "none of these words" field.

Furthermore, the author in [20] studied the Boundary value problem with fractional p-Laplacian operator by using the mountain pass theorem.

Recently, the authors in [19] considered the existence of periodic and subharmonic solutions for the nonlinear difference equations with p-Laplace operator by using the saddle point theorem.

First, we establish some sharp inequalities for the Toeplitz type operator T b, and, second, we prove the boundedness for the Toeplitz type operator by using the sharp inequalities.

Recently, Nair [37] introduced the pathway fractional integral operator by using the pathway idea of Mathai [6], developed further by Mathai and Haubold [38] and defined as follows (cf. [39]).

The object of the present paper is to investigate some inclusion relations and other interesting properties for certain classes of p-valent functions involving generalized Srivastava-Attiya operator by using the principle of differential subordination.

We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem.

Furthermore, we obtain the convergence of the operators by using the modulus of continuity and prove some direct theorems.

We calculate the error of approximation of these operators by using the modulus of continuity and Lipschitz-type functionals.

We also find conditions to obtain the corresponding subclasses of compact matrix operators by using the Hausdorff measure of noncompactness.

In Section 4, we obtain the approximate controllability for nonlinear evolution equation (1.1) with hemicontinuous monotone operators by using the theory of monotone operators.