A Generalization of Tyuriemskih's Lethargy Theorem and Some Applications
Authors:
- 7 March 2013
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 34 (9) , 1033-1040
Abstract
Tyuriemskih's Lethargy Theorem is generalized to provide a useful tool for establishing when a sequence of (not necessarily) linear operators that converges point wise to the identity operator actually converges arbitrarily slowly. Then this generalization is used to answer affirmatively a 2010 conjecture of ours as well as establishing that all of the classical operators of Bernstein, Hermite-Fejer, Landau, Fejer, and Jackson converge arbitrarily slowly to the identity operator (and not just almost arbitrarily slowly as we established in 2010).Keywords
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