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

2011 ◽  
Vol 218 (6) ◽  
pp. 2960-2967
Author(s):  
Harun Karsli ◽  
Paulina Pych-Taberska
Keyword(s):  
Rates Of Convergence ◽  
Kantorovich Operators ◽  
Bézier Variant

On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant

2009 ◽  
Vol 16 (4) ◽  
pp. 693-704
Author(s):  
Harun Karsli ◽  
Paulina Pych-Taberska
Keyword(s):  
Recent Result ◽  
Pointwise Convergence ◽  
Rates Of Convergence ◽  
Durrmeyer Operators ◽  
The One ◽  
Special Case ◽  
Appl Math ◽  
Bézier Variant

Abstract We consider the Bézier variant of Chlodovsky–Durrmeyer operators 𝐷𝑛,α for functions 𝑓 measurable and locally bounded on the interval [0,∞). By using the Chanturia modulus of variation we estimate the rate of pointwise convergence of (𝐷𝑛,α 𝑓) (𝑥) at those 𝑥 > 0 at which the one-sided limits 𝑓(𝑥+), 𝑓(𝑥–) exist. In the special case α = 1 the recent result of [Ibikli, Karsli, J. Inequal. Pure Appl. Math. 6: 12, 2005] concerning the Chlodovsky–Durrmeyer operators 𝐷𝑛 is essentially improved and extended to more general classes of functions.

scholarly journals Rate of approximation for the Bézier variant of Balazs Kantorovich operators

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Vijay Gupta ◽  
X. Zeng
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Rate Of Approximation ◽  
Kantorovich Operators ◽  
Bézier Variant

AbstractIn the present paper we study the Bézier variant of the well known Balazs-Kantorovich operators L n,α(f,x), α ≥ 1. We establish the rate of convergence for functions of bounded variation. For particular value α = 1, our main theorem completes a result due to Agratini [Math. Notes (Miskolc) 2 (2001), 3–10].

Approximation by Bézier variant of the Szász–Kantorovich operators in case α < 1

2010 ◽  
Vol 17 (2) ◽  
pp. 253-260
Author(s):  
Vijay Gupta ◽  
Xiao-Ming Zeng
Keyword(s):  
Bounded Variation ◽  
Convergence Theorem ◽  
Functions Of Bounded Variation ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Type Approximation ◽  
Bounded Functions ◽  
Kantorovich Operators ◽  
Special Case ◽  
Bézier Variant

Abstract The present paper deals with the Bézier variant of the Szász–Kantorovich operator. Its approximation properties are studied. A convergence theorem of this type approximation operators for locally bounded functions is established, which subsumes the approximation of functions of bounded variation as a special case.

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