The degree of monotone approximation

R. K. Beatson

Vol. 74 (1978), No. 1, 5–14

DOI: 10.2140/pjm.1978.74.5

Abstract

Jackson type theorems are obtained for generalized monotone approximation. Let E_n,k(f) be the degree of approximation of f by n-th degree polynomials with k-th derivative nonnegative on [−1∕4,1∕4]. Then for each k ≧ 2 there exists an absolute constant D_k, such that for all f ∈ C[−1∕4,1∕4] with k-th difference nonnegative on [−1∕4,1∕4]; E_n,k(f) ≦ D_kω(f,n⁻¹). If in addition f′∈ C[−1∕4,1∕4] then E_n,k(f) ≦ D_kn⁻¹ω(f′,n⁻¹).

Mathematical Subject Classification 2000

Primary: 41A10

Milestones

Received: 28 April 1977

Published: 1 January 1978