A problem of I. Raşa on Bernstein polynomials and convex functions
Abstract
We present an elementary proof of a conjecture by I. Raşa 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-Szász operators and Baskakov operators.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2016
- DOI:
- 10.48550/arXiv.1609.00234
- arXiv:
- arXiv:1609.00234
- Bibcode:
- 2016arXiv160900234A
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 26D05;
- 39B62