Sentence examples for applications of the operator from inspiring English sources

Some applications of the operator J s, b ( f ) to certain classes in Geometric Function Theory can be found in [14 16] and [17].

Inspired by their work, in this paper, we construct two generalized q-exponential operator with three parameters and give some operator identities to further investigate the applications of the operator technique.

Further, a proper set of conditions has been discussed to rectify the errors and applications pointed out in Remarks 1 and 2. Some interesting applications of the operator used in this paper were pointed out in Note 1.

In the framework discussed in Section  1 this means that we have to bound at least three applications of the operator b (u ⋆ ) to the exact solution.

Note that in the linear case this assumption is equivalent to the fact that b 3 u (t ) can be bounded; i.e., we have to bound three applications of the operator b to the exact solution.

In [18], in the class of harmonic functions in a ball, the properties and applications of the operators in the form of δ μ = r ∂ ∂ r + μ, δ μ m = ( r ∂ ∂ r + μ ) m (6).

It should be noted that properties and applications of the operators B α, B ∗ α and B − α in the class of harmonic functions in the ball Ω are studied in [10].

The whole analysis may be performed by a repeated application of the operator.

Some interesting application of the operator ( C 1 ⋅ N p ) used in this paper is pointed out in Note 3.4.

The application of the operator splitting permits the isolation of the nonlinear part of the equation that is solved by explicit Adams-Bashforth time marching for half the time step.

By a change of variable and the definition of c δ, we have again: Remark 2. Observe that: As an application of the operator fractional derivative D δ, we will give a characterization of the potential spaces, which is simpler and more powerful, valid for any 1