A solution to the problem of Rasa connected with Bernstein polynomials
Analysis of PDEs
2016-04-26 v1
Abstract
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.
Cite
@article{arxiv.1604.07381,
title = {A solution to the problem of Rasa connected with Bernstein polynomials},
author = {Jacek Mrowiec and Teresa Rajba and Szymon Wasowicz},
journal= {arXiv preprint arXiv:1604.07381},
year = {2016}
}