Sentence examples for regularizing functions from inspiring English sources

In this paper, by employing tensor products of regularizing functions as in [7, 8], we consider the regularity of the solutions of (1.3) and prove in an elementary way that (1.3) can be reduced to the classical equation (1.1) of smooth functions.

Using the regularizing functions, Chung [17] extended the stability theorem of the Cauchy functional equation (1.1) to the space D ′ ( ℝ m ).

Moreover, using the regularizing functions, we extend these results to the space of distributions.

Moreover, using the Dirac sequence of regularizing functions, we extend these results to the space of distributions.

Subsequently, in Section 3, making use of the Dirac sequence of regularizing functions, we extend these results to the space D ′.

Needless to say that convexity of the regularizing functions avoids the presence of local minima, and allows for solving the resulting optimization problem efficiently.

Usually, we call ψ(x) to the regularizing function.

For an example of function ρ whose regularizing function σ satisfy (h3) we can refer to [17].

We call a regularizing function of the distribution, since is a smooth function of satisfying in the sense of distributions, that is, for every, (3.2).

Depending on the peculiarity of equation, ill-posed problem is generally resolved via constructing an additional regularizing function to resume stability [23, 24].

With small and positive value, parameter β is regulated to ensure that regularizing function J β (F) is differentiable at F = 0.