Convergence in Variation for Bernstein-Type Operators

İNCE İLARSLAN H. G., Bascanbaz-Tunca G.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.13, sa.5, ss.2577-2592, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 5
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00009-015-0640-1
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2577-2592
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we deal with Bernstein-type operators defined by Cardenas-Morales et al. as , where is the nth Bernstein polynomial (Comput Math Appl 62(1):158-163, 2011). Assuming that and f are absolutely continuous functions on and inf as well as and we study the convergence of Bernstein-type operators to f in variation seminorm. Moreover, we give a Voronovskaja-type formula and a Jackson-type estimate in the sense of Bardaro et al. (Analysis 23:299-340, 2003).