Upper bounds for Bernstein basis functions. (English) Zbl 1270.41008
Shiryaev, Albert N. (ed.) et al., Prokhorov and contemporary probability theory. In honor of Yuri V. Prokhorov on the occasion of his 80th birthday. Berlin: Springer (ISBN 978-3-642-33548-8/hbk; 978-3-642-33549-5/ebook). Springer Proceedings in Mathematics & Statistics 33, 293-301 (2013).
Summary: Starting with Markov bounds for binomial coefficients (for which a short proof is given), upper bounds are derived for Bernstein basis functions of approximation operators and their maximum. Some related inequalities used in approximation theory and those for concentration functions are discussed.
For the entire collection see [Zbl 1258.60006].
For the entire collection see [Zbl 1258.60006].
MSC:
| 41A36 | Approximation by positive operators |
| 41A44 | Best constants in approximation theory |
| 60E15 | Inequalities; stochastic orderings |
| 60G50 | Sums of independent random variables; random walks |
Keywords:
Bernstein basis functions for approximation operators; Markov bounds; binomial coefficients; Zeng’s upper bounds; Rogozin’s inequality; inequalities for concentration functionsReferences:
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