Some properties of the Bézier–Kantorovich type operators |
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Authors: | Paulina Pych-Taberska |
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Affiliation: | Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61–614, Pozna , Poland |
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Abstract: | The aim of this paper is to present estimates for the rate of pointwise convergence of the Bézier–Kantorovich modification of the discrete Feller operators in some classes of measurable functions bounded on an interval I, in particular, for functions of bounded pth power variation on I. Our theorems generalize and extend the recent results of Zeng and Piriou (J. Approx. Theory 95(1998) 369; 104(2000) 330) for the kantorovichians of the Bernstein–Bézier operators in the class of functions of bounded variation in the Jordan sense on [0,1]. |
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Keywords: | Discrete Feller operator Kantorovich and Bé zier type operator Rate of pointwise convergence Modulus of variation pth Power variation |
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