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On the monotonicity property for the sequence of classical Bernstein operators

  • Dan Miclăuş
Article
  • 14 Downloads

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.

Keywords

Bernstein operator Divided difference Convex function Monotonicity Popoviciu theorem Remainder term 

Mathematics Subject Classification

26A51 26D15 41A36 41A80 

Notes

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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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnical University of Cluj-Napoca, North University Center at Baia MareBaia MareRomania

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