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2 Commentationes Mathematicae

2 2009

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

100%

Pych-Taberska P. , Karsli H.

tom Vol. 49, [Z] 2

189-208

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

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

100%

Pych-Taberska P. , Karsli H.

tom 49

nr 2

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.