arXiv subjects

Jacek Mrowiec

Publications and source records attributed to Jacek Mrowiec.

2 recordsLinked to original sources

arXiv2016

On the classes of higher-order Jensen-convex functions and Wright-convex functions, II

Recently Nikodem, Rajba and Wąsowicz compared the classes of n-Wright-convex functions and n-Jensen-convex functions by showing that the first one is a proper subclass of the latter one, whenever n is an odd natural number. Till now the case of even n was an open problem. In this paper the complete solution is given: it is shown that the inclusion is proper for any natural n. The classes of strongly n-Wright-convex and strongly n-Jensen-convex functions are also compared (with the same assertion).

math.CA↗

arXiv2016

A solution to the problem of Rasa connected with Bernstein polynomials

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.

math.AP↗