Degree of Uniform Approximation by Multivariate Generalized Discrete Singular Operators
Here we establish the uniform approximation properties of multivariate generalized discrete versions of Picard, Gauss. Weierstrass, and Poisson. Cauchy singular operators over ℝN, N ≥ 1. We treat both the unitary and non-unitary cases of the operators above. We give quantitatively the pointwise and uniform convergences of these operators to the unit operator by involving the multivariate higher order modulus of smoothness. It follows .
Series on Concrete and Applicable Mathematics
Anastassiou, G., & Kester, M. (2017). Degree of Uniform Approximation by Multivariate Generalized Discrete Singular Operators. Series on Concrete and Applicable Mathematics, 20, 181-211. https://doi.org/10.1142/9789813145849_0007