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arXiv · 1604.07381

A solution to the problem of Rasa connected with Bernstein polynomials

Jacek Mrowiec·Teresa Rajba·Szymon Wasowicz
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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.

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Jacek Mrowiec, Teresa Rajba, Szymon Wasowicz. 2016-04-25. A solution to the problem of Rasa connected with Bernstein polynomials. https://arxiv.org/abs/1604.07381

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