Filomat 2022 Volume 36, Issue 18, Pages: 6129-6138
https://doi.org/10.2298/FIL2218129B
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On Stancu operators depending on a non-negative integer
Bostancı Tuğba (Ankara University, Faculty of Science, Department of Mathematics, Beşevler, Ankara, Turkey + National Defence University, Naval Petty-Officer Vocational School, Basic Sciences Department, Altınova, Yalova, Turkey), tbostanci@ankara.edu.tr; bostanci.tugba06@gmail.co
Başcanbaz-Tunca Gülen (Ankara University, Faculty of Science, Department of Mathematics, Beşevler, Ankara, Turkey), tunca@science.ankara.edu.tr
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 < ∞, 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.
Keywords: Stancu operator depending on a non-negative integer, Kantorovich operators, Lp-convergence, Averaged modulus of smoothness, Variation detracting property, Convergence in variation seminorm
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