APPROXIMATION PROPERTIES OF RIEMANN-LIOUVILLE TYPE FRACTIONAL BERNSTEIN-KANTOROVICH OPERATORS OF ORDER - Baytunc, Erdem; Aktuglu, Huseyin; Mahmudov, Nazim I. (Amer Inst Mathematical Sciences-Aims, 2024)
. 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.
Keywords: Bernstein-Kantorovich operators; rate of convergence; modulus of continuity; bivariate Bernstein-Kantorovich operators; affine functions; positive linear operators