A Generalization of Tyuriemskih's Lethargy Theorem and Some Applications

作者：Deutsch Frank^*; Hundal Hein

来源：Numerical Functional Analysis and Optimization, 2013, 34(9): 1033-1040.

DOI：10.1080/01630563.2012.761636

• Approximation by positive operators
• Arbitrarily slow convergence of linear operators
• Bernstein operators
• Fejer operators
• Hermite-Fejer operators
• Jackson operators
• Landau operators
• Lethargy theorem
• 41A25
• 41A65
• 41A36

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).

• 出版日期2013-9-2