A solution to the problem of Rasa connected with Bernstein polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Mrowiec, Jacek¹  Rajba, Teresa¹  Wasowicz, Szymon¹ 

[1] Univ Bielsko Biala, Dept Math, Willowa 2, PL-43309 Bielsko Biala, Poland

关键词: Bernstein polynomials;    Stochastic ordering;    Ohlin's Lemma;    Concentration inequality;    Convex functions;    Bernoulli and binomial distributions;   

DOI  :  10.1016/j.jmaa.2016.09.009

来源: Elsevier

【 摘 要 】

During the Conference on Ulam's Type Stability (Rytro, Poland, 2014), Ioan Rasa recalled his 25-years-old problem concerning some inequality involving the Bernstein polynomials. We offer the complete solution (in positive). As a tool we use stochastic orderings (which we prove for binomial distributions) as well as so-called concentration inequality. Our methods allow us to pose (and solve) the extended version of the problem in question. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free