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

Paulina Pych-Taberska;  Harun Karsli — 2009

Commentationes Mathematicae

In the present paper we consider the Bézier variant of Chlodovsky-Kantorovich operators K n − 1 , α f for functions f measurable and locally bounded on the interval [ 0 , ∞ ) . By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of K n − 1 , α f ( x ) at those x 0 at which the one-sided limits f ( x + ) , f ( x - ) exist.

Voronovskaya-Type Theorems for Derivatives of the Bernstein-Chlodovsky Polynomials and the Szász-Mirakyan Operator

Paul Leo Butzer;  Harun Karsli — 2009

Commentationes Mathematicae

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 b n 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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