Strong Inequalities for Weighted Approximation by Hermite-Fejer Interpolation

摘要

We study Hermite-Fejer interpolation operators in spaces of weighted maximum norm, whose nodes are the zeros of Jacobi polynomials with indexes alpha, beta > -1. The approximation behaviour of those operators is presented by the so-called strong inequalities. Moreover, such strong inequalities are valid for any individual continuous function on [-1,1]. The obtained result covers also the saturation of these operators.