Rate of Approximation of Bounded Variation Functions by the Bézier Variant of Chlodowsky Operators
نویسندگان
چکیده
In this paper the pointwise approximation of the Bézier variant of Chlodowsky operators for bounded variation functions is studied. By means of the analysis techniques and some results of probability theory, we obtain an estimate formula on this type approximation. Our results correct the mistake of Karsli and Ibikli [H. Karsli and E. Ibikli, Convergence rate of a new Bézier variant of Chlodowsky operators to bounded variation functions, J. Comput. Appl. Math 212 (2008) 431–443], and also extend the work of Zeng [X. M. Zeng, On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions II, J. Approx. Theory 104 (2000) 330–344]. Mathematics subject classification (2010): 41A36, 41A25, 41A10.
منابع مشابه
On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...
متن کاملSimultaneous approximation for Bézier variant of Szász–Mirakyan–Durrmeyer operators
We study the rate of convergence in simultaneous approximation for the Bézier variant of Szász– Mirakyan–Durrmeyer operators by using the decomposition technique of functions of bounded variation. © 2006 Elsevier Inc. All rights reserved.
متن کاملSimultaneous Approximation for the Phillips-bézier Operators
We study the simultaneous approximation properties of the Bézier variant of the well known Phillips operators and estimate the rate of convergence of the Phillips-Bézier operators in simultaneous approximation, for functions of bounded variation.
متن کاملConvergence rate of a new Bezier variant of Chlodowsky operators to bounded variation functions
In the present paper, we estimate the rate of pointwise convergence of the Bézier Variant of Chlodowsky operators Cn, for functions, defined on the interval extending infinity, of bounded variation. To prove our main result, we have used some methods and techniques of probability theory. © 2007 Elsevier B.V. All rights reserved. MSC: 41A25; 41A35; 41A36
متن کاملBézier Variant of Modified Srivastava–gupta Operators
Srivastava and Gupta proposed in 2003 a general family of linear positive operators which include several well known operators as its special cases and investigated the rate of convergence of these operators for functions of bounded variation by using the decomposition techniques. Subsequently, researchers proposed several modifications of these operators and studied their various approximation...
متن کامل