Optimal approximation class for multivariate Bernstein operators

Zeev Ditzian and Xinlong Zhou

Vol. 158 (1993), No. 1, 93–120

DOI: 10.2140/pjm.1993.158.93

Abstract

For the Bernstein polynomial approximation process on a simplex or a cube, the class of functions yielding optimal approximation will be given. That is, we will find the class of functions for which ∥B_nf − f∥_C(S) = O(n⁻¹) in terms of the behaviour of a certain K-functional. Moreover, this is done in the context of direct and converse results which yields an improvement on such results as well.

Mathematical Subject Classification 2000

Primary: 41A36

Secondary: 41A63

Milestones

Received: 17 June 1991

Published: 1 March 1993