APPROXIMATION PROPERTIES OF RIEMANN-LIOUVILLE TYPE FRACTIONAL BERNSTEIN-KANTOROVICH OPERATORS OF ORDER

Abstract

. In this paper, we construct a new sequence of Riemann-Liouville type fractional Bernstein-Kantorovich operators Kn & alpha;(f; x) depending on a parameter & alpha;. We prove a Korovkin type approximation theorem and discuss the rate of convergence with the first and second order modulus of continuity of these operators. Moreover, we introduce a new operator that preserves affine functions from Riemann-Liouville type fractional Bernstein-Kantorovich operators. Further, we define the bivariate case of Riemann-Liouville type fractional Bernstein-Kantorovich operators and investigate the order of convergence. Some numerical results are given to illustrate the convergence of these operators and its comparison with the classical case of these operators.