Abstract
This note presents the proof of monotonicity property for the sequence of classical Bernstein operators, involving divided differences and convex functions. As application, we get the form of remainder term associated to the classical Bernstein operators applying Popoviciu’s theorem. We also shall establish an upper bound estimation for the remainder term, when approximated function fulfills some given properties.
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Acknowledgements
The results presented in this paper were obtained with the support of the Technical University of Cluj-Napoca through the research Contract No. 2011 / 12.07.2017, Internal Competition CICDI-2017.
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Miclăuş, D. On the monotonicity property for the sequence of classical Bernstein operators. Afr. Mat. 29, 1141–1149 (2018). https://doi.org/10.1007/s13370-018-0602-4
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DOI: https://doi.org/10.1007/s13370-018-0602-4