Vol. 74, No. 1, 1978

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ISSN: 0030-8730
The degree of monotone approximation

R. K. Beatson

Vol. 74 (1978), No. 1, 5–14
Abstract

Jackson type theorems are obtained for generalized monotone approximation. Let En,k(f) be the degree of approximation of f by n-th degree polynomials with k-th derivative nonnegative on [14,14]. Then for each k 2 there exists an absolute constant Dk, such that for all f C[14,14] with k-th difference nonnegative on [14,14]; En,k(f) Dkω(f,n1). If in addition f′∈ C[14,14] then En,k(f) Dkn1ω(f,n1).

Mathematical Subject Classification 2000
Primary: 41A10
Milestones
Received: 28 April 1977
Published: 1 January 1978
Authors
R. K. Beatson