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Preliminaries Read chapter Read first chapter

2014 | OriginalPaper | Chapter

8. Convergence for Bounded Functions on Bézier Variants

Authors : Vijay Gupta, Ravi P. Agarwal

Published in: Convergence Estimates in Approximation Theory

Publisher: Springer International Publishing

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Abstract

The various Bézier variants (BV) of the approximation operators are important research topics in approximation theory. They have close relationships with geometry modeling and design. Let \(p_{n,k}(x) = \left (\begin{array}{c} n\\ k \end{array} \right ){x}^{k}{(1-x)}^{n-k},(0 \leq k \leq n)\) be Bernstein basis functions. The Bézier basis functions, which were introduced in 1972 by Bézier [39], are defined as \(J_{n,k}(x) =\sum _{ j=k}^{n}p_{n,j}(x)\).

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previous chapter Rate of Convergence for Functions of Bounded Variation
next chapter Some More Results on the Rate of Convergence
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Metadata
Title
Convergence for Bounded Functions on Bézier Variants
Authors
Vijay Gupta
Ravi P. Agarwal
Copyright Year
2014
Book
Convergence Estimates in Approximation Theory

Print ISBN: 978-3-319-02764-7

Electronic ISBN: 978-3-319-02765-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-02765-4_8

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