Simultaneous weighted approximation with multivariate Baskakov–Schurer operators

Abstract

We study the properties of weighted simultaneous approximation of multivariate Baskakov–Schurer operators. We obtain quantitative estimates with explicit constants of the weighted approximation error for the partial derivatives. Moreover, we analyze the behavior of the operators with respect to weighted Lipschitz functions. For this purpose, we first compute the best constants, M ϵ ℝ, in the inequalities of the type An,p ((1 + |t|)r) ≤ M (1 +|t|)r.