In this paper we establish an estimation for the rate of pointwise convergence of the Chlodovsky-Kantorovich polynomials for functions f locally integrable on the interval [0,∞). In particular, corresponding estimation for functions f measurable and locally bounded on [0,∞) is presented, too.

The smoothness and approximation properties of certain discrete operators for bivariate functions are examined.

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 $[0,\infty )$. By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of ${K}_{n-1,\alpha}f\left(x\right)$ at those $x0$ at which the one-sided limits $f(x+)$, $f(x-)$ exist.

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