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