On the rates of convergence of Chlodovsky-Kantorovich operators and their Bézier variant

In the present paper we consider the Bézier variant of Chlodovsky-Kantorovich operators $K_{n-1,\alpha }f$ for functions $f$ measurable and locally bounded on the interval $[0,\mathrm{\infty })$. By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of $K_{n-1,\alpha }f(x)$ at those $x>0$ at which the one-sided limits $f(x+)$, $f(x-)$ exist.