On Stancu Operators Depending on a Non-Negative Integer

Bostanci T., Bascanbaz-Tunca G.

FILOMAT, vol.36, no.18, pp.6129-6138, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 18
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2218129b
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.6129-6138
  • Keywords: (Stancu operator depending on a non-negative integer, Kantorovich operators, Lp-convergence, Averaged modulus of smoothness, Variation detracting property, Convergence in variation seminorm
  • Ankara University Affiliated: Yes

Abstract

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.