Uniform approximation with rates 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 convergence of these operators to the unit operator by involving the multivariate higher order modulus of smoothness.

Publication Title

Springer Proceedings in Mathematics and Statistics