A Kantorovich variant of a generalized Bernstein operators

Abstract

In this note we present a Kantorovich variant of the operators proposed by [X. Y. Chen, J. Q. Tan, Z. Liu, J. Xie, J. Math. Anal. Appl., 450 (2017), 244-261] based on non-negative parameters. Here, we prove an approximation theorem with the help of Bohman-Korovkin's principle and study the estimate of the rate of approximation by using the modulus of smoothness and Lipschitz type function for these operators. Also, we establish Voronovskaja type theorem and Korovkin type A-statistical approximation theorem of these operators.