Degree of Lp Approximation by Generalized Discrete Singular Operators Here

Here we give 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 the operators above. We derive quantitatively Lp convergence of these operators to the unit operator by involving the Lp higher modulus of smoothness of an Lp(ℝ) function. It follows [4]