APPROXIMATION OF FUNCTIONS BY GENUINE BERNSTEIN-DURRMEYER TYPE OPERATORS


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ACAR T., Acu A. M. , Manav N.

JOURNAL OF MATHEMATICAL INEQUALITIES, vol.12, no.4, pp.975-987, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.7153/jmi-2018-12-74
  • Title of Journal : JOURNAL OF MATHEMATICAL INEQUALITIES
  • Page Numbers: pp.975-987

Abstract

Very recently, in [4] Chen et. al introduced and considered a new generalization of Bernstein polynomials depending on a patameter alpha. As classical Bernstein operators, these operators also provide interpolation at the end points of [0,1] and they have the linear precision property which means those reproduce the linear functions. In this paper we introduce genuine alpha-Bernstein-Durrmeyer operators. Some approximation results, which include local approximation, error estimation in terms of Ditzian-Totik modulus of smoothness are obtained. Also, the convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.