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.
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 \(K_{n−1,\alpha} f (x)\) at those \(x \gt 0\) at which the one-sided limits \(f (x+)\), \(f(x-)\) exist.
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