Convergence of the Bernstein-Durrmeyer Operators in Variation Seminorm

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KARSLI H., Yilik O. O., TAŞDELEN YEŞİLDAL F.

RESULTS IN MATHEMATICS, cilt.72, sa.3, ss.1257-1270, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00025-017-0653-0
  • Dergi Adı: RESULTS IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1257-1270
  • Anahtar Kelimeler: Approximation in variation, absolutely continuous functions, Bernstein-Durrmeyer operators, APPROXIMATION, POLYNOMIALS
  • Ankara Üniversitesi Adresli: Evet

Özet

The aim of this paper is to study variation detracting property and convergence in variation of the Bernstein-Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are studied with respect to the variation seminorm. Moreover we also study the rate of convergence in terms of total variation.