APPROXIMATION OF FUNCTIONS BY GENUINE BERNSTEIN-DURRMEYER TYPE OPERATORS

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

JOURNAL OF MATHEMATICAL INEQUALITIES, cilt.12, sa.4, ss.975-987, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.7153/jmi-2018-12-74
  • Dergi Adı: JOURNAL OF MATHEMATICAL INEQUALITIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.975-987
  • Anahtar Kelimeler: Genuine Bernstein-Durrmeyer operators, rate of convergence, linear positive operators
  • Gazi Üniversitesi Adresli: Evet

Özet

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.