Some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of \(\alpha\)

Abstract

The main intent of this paper is to examine some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of \(\alpha\). We derive some moment estimates and show the uniform convergence theorem, degree of convergence with respect to the usual modulus of continuity, class of Lipschitz-type continuous functions and as well as Peetre’s K-functional. Furthermore, we present various graphical and numerical examples to demonstrate and compare the effectiveness of the proposed operators. Also, we construct bivariate extension of the related operators and consider order of approximation by means of partial and complete modulus of continuity. Further, we provide a graphical representation and an error of approximation table to show the behavior order of convergence of bivariate form of discussed operators.