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    On the rates of convergence of BBH-Kantorovich operators and their Bezier variant
    (Elsevier Science Inc, 2011) Karslı, Harun; Pych-Taberska, Paulina
    In the present paper we consider the Bezier variant of BBH-Kantorovich operators J(n,alpha)f for functions f measurable and locally bounded on the interval [0, infinity) with alpha >= 1. By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of J(n,alpha)f(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, Journal of Inequalities and Applications 2009 (2009) 10 (Article ID 852897)] is extended to more general classes of functions. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.
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    On the rates of convergence of Bernstein-Chlodovsky polynomials and their Bezier-type variants
    (Taylor & Francis Ltd, 2011) Pych-Taberska, Paulina; Karslı, Harun
    In this article, we consider the Chlodovsky polynomials Cn f and their Bezier variants Cn, f, with 0, for locally bounded functions f on the interval [0, ). Using the Chanturiya modulus of variation we give estimates for the rates of convergence of Cn f (x) and Cn, f (x) at those points x 0 at which the one-sided limits f (x+), f (x-) exist. The recent results of Karsli and Ibiki [H. Karsli and E. Ibikli, Rate of convergence of Chlodovsky type Bernstein operators for functions of bounded variation, Numer. Funct. Anal. Optim. 28(3-4) (2007), pp. 367-378; H. Karsli and E. Ibikli, Convergence rate of a new Bezier variant of Chlodovsky operators to bounded variation functions, J. Comput. Appl. Math. 212(2) (2008), pp. 431-443.] are essentially improved and extended to more general classes of functions.
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    On the rates of convergence of Chlodovsky-Durrmeyer operators and their Bézier variant
    (2009) Karslı, Harun; Pych-Taberska, Paulina
    We consider the Bézier variant of Chlodovsky-Durrmeyer operators Dn,? for functions/measurable and locally bounded on the interval [0, ?). By using the Chanturia1 modulus of variation we estimate the rate of pointwise convergence of (Dn,?f) (x) at those x > 0 at which the one-sided limits f(x+), f(x-) exist. In'the special case ? = 1 the recent result of [14] concerning the Chlodovsky-Durrmeyer operators Dn is essentially improved and extended to more general classes of functions. © Heldermann Verlag.
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    ON THE RATES OF CONVERGENCE OF CHLODOVSKY-DURRMEYER OPERATORS AND THEIR BEZIER VARIANT
    (Walter De Gruyter Gmbh, 2009) Karsli, Harun; Pych-Taberska, Paulina
    We consider the Bezier variant of Chlodovsky-Durrmeyer operators D-n,D-alpha for functions f measurable and locally bounded on the interval [0, infinity). By using the Chanturia(1) modulus of variation we estimate the rate of pointwise convergence of (D(n,alpha)f) (x) at those x > 0 at which the one-sided limits f (x+), f (x-) exist. In the special case alpha = 1 the recent result of [14] concerning the Chlodovsky Durrmeyer operators D-n is essentially improved and extended to more general classes of functions.