On Kantorovich variant of Brass-Stancu operators

Abstract

In this study, we deal with Kantorovich-type generalization of the Brass-Stancu operators. For the sequence of these operators, we study L- p-convergence and give some upper estimates for the L- p-norm of the approximation error via first-order averaged modulus of smoothness and the first-order K K -functional. Moreover, we show that the Kantorovich generalization of each Brass-Stancu operator satisfies variation detracting property and is bounded with respect to the norm of the space of functions of bounded variation on [ 0 , 1 ]. Finally, we present graphical and numerical examples to compare the convergence of these operators to given functions under different parameters.