Rate of convergence of Chlodowsky operators for functions with derivatives of bounded variation.
In the present paper we consider the Bézier variant of Chlodovsky-Kantorovich operators for functions measurable and locally bounded on the interval . By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of at those at which the one-sided limits , exist.
This paper is devoted to a study of a Voronovskaya-type theorem for the derivative of the Bernstein–Chlodovsky polynomials and to a comparison of its approximation effectiveness with the corresponding theorem for the much better-known Szász–Mirakyan operator. Since the Chlodovsky polynomials contain a factor tending to infinity having a certain degree of freedom, these polynomials turn out to be generally more efficient in approximating the derivative of the associated function than does the Szász...
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