• Corpus ID: 119165421

A problem of I. Ra\c{s}a on Bernstein polynomials and convex functions

  title={A problem of I. Ra\c\{s\}a on Bernstein polynomials and convex functions},
  author={Ulrich Abel},
  journal={arXiv: Classical Analysis and ODEs},
  • U. Abel
  • Published 27 August 2016
  • Mathematics
  • arXiv: Classical Analysis and ODEs
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-Szasz operators and Baskakov operators. 


A solution to the problem of Raşa connected with Bernstein polynomials
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
Convex Functions and Their Applications: A Contemporary Approach
This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some o
Niculescu and Lars - Erik Persson , Convex functions and their applications
  • CMS Books in Mathematics / Ouvrages de Mathématiques de la SMC
  • 2006
Stečkin, Inequalities, Amer.Math
  • Soc. Transl. (2),
  • 1960