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A solution to the problem of Raşa connected with Bernstein polynomials

Author:
Jacek Mrowiec  Teresa Rajba  Szymon Wąsowicz  


Journal:
Journal of Mathematical Analysis and Applications


Issue Date:
2017


Abstract(summary):

Abstract During the Conference on Ulam's Type Stability (Rytro, Poland, 2014), Ioan Raşa 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.


Page:
864-864


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