On Stancu operators depending on a non-negative integer

Abstract

In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, we consider Kantorovich extension of the operators. By the sequence of these Stancu-Kantorovich operators, attached to functions belonging to the space L^{p}[0,1], 1≤p<∞, we obtain convergence in the norm of L^{p}. Finally, we give an estimate for the rate of the convergence via first order averaged modulus of smoothness. Moreover, we search variation detracting property for the Stancu operators for the functions of bounded variation on [0,1] and also present the convergence in variation seminorm by these operators when the operand is absolutely continuous on [0,1].