Degree of Uniform Approximation by Generalized Discrete Singular Operators
Here we study the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. We treat both the unitary and non-unitary cases of these operators. We establish quantitatively the pointwise and uniform convergences of these operators to the unit operator by involving the uniform higher modulus of smoothness of a uniformly continuous function. It follows .
Series on Concrete and Applicable Mathematics
Anastassiou, G., & Kester, M. (2017). Degree of Uniform Approximation by Generalized Discrete Singular Operators. Series on Concrete and Applicable Mathematics, 20, 1-25. https://doi.org/10.1142/9789813145849_0001