Global smoothness preservation and simultaneous approximation by multivariate discrete operators

Abstract

In this article we study the multivariate generalized discrete singular operators defined on R N , N ≥ 1, regarding their simultaneus global smoothness preservation property with respect to Lp norm for 1 ≤ p ≤ ∞, by using higher order moduli of smoothness. Furthermore, we study their simultaneous approximation properties.