On Stancu Operators Depending on a Non-Negative Integer

Bostanci T., Bascanbaz-Tunca G.

FILOMAT, cilt.36, sa.18, ss.6129-6138, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 18
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2218129b
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.6129-6138
  • Anahtar Kelimeler: (Stancu operator depending on a non-negative integer, Kantorovich operators, Lp-convergence, Averaged modulus of smoothness, Variation detracting property, Convergence in variation seminorm
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, we define Kantorovich extension of the operators. For functions belonging to the space Lp [0,1] , 1 <= p < infinity, we obtain convergence in the norm of Lp by the sequence of Stancu-Kantorovich operators, and we give an estimate for the rate of the convergence via first order averaged modulus of smoothness. Moreover, for the Stancu operators; we search variation detracting property and convergence in the space of functions of bounded variation in the variation seminorm.