An interpolation theorem and its applications to positive operators

Vilmos Totik

Vol. 111 (1984), No. 2, 447–481

DOI: 10.2140/pjm.1984.111.447

Abstract

We answer a special case of a problem of Z. Ditzian. The obtained estimate for the Peetre K functional is applied to the characterization of functions for which ∥T_nf − f∥ = O(n^−α) (0 < α < 1), where T_n is either the Bernstein, Szász-Mirakjan or Baskakov operator or their Kantorovich-invariant and ∥⋅∥ denotes either the L^p (p ≥ 1) or the supremum norm.

Mathematical Subject Classification 2000

Primary: 41A27

Secondary: 46M35

Milestones

Received: 21 July 1982

Published: 1 April 1984