A problem of I. Rasa on Bernstein polynomials and convex functions
Abstract
We present an elementary proof of a conjecture by I. Rasa which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover, we derive the corresponding results for Mirakyan-Favard-Sz\'asz operators and Baskakov operators.
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