On the rates of convergence of BBH-Kantorovich operators and their Bézier variant |
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| Authors: | Harun Karsli Paulina Pych-Taberska |
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| Institution: | a Abant Izzet Baysal University, Faculty of Science and Arts, Department of Mathematics, 14280 Bolu, Turkey
b Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan´, Poland |
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| Abstract: | In the present paper we consider the Bézier variant of BBH-Kantorovich operators Jn,αf for functions f measurable and locally bounded on the interval 0, ∞) with α ? 1. By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of Jn,αf(x) at those x > 0 at which the one-sided limits f(x+), f(x−) exist. The very recent result of Chen and Zeng (2009) L. Chen, X.M. Zeng, Rate of convergence of a new type Kantorovich variant of Bleimann-Butzer-Hahn Operators, J. Inequal. Appl. 2009 (2009) 10. Article ID 852897] is extended to more general classes of functions. |
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| Keywords: | Rate of convergence BBH-Kantorovich operator Bé zier basis Chanturiya&rsquo s modulus of variation pth power variation |
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