Convergence for Bounded Functions on Bézier Variants

Vijay Gupta and Ravi P. Agarwal
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Vijay Gupta: Netaji Subhas Institute of Technology, School of Applied Sciences
Ravi P. Agarwal: Texas A&M University - Kingsville, Department of Mathematics

Chapter Chapter 8 in Convergence Estimates in Approximation Theory, 2014, pp 249-286 from Springer

Abstract: 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 Bézier basis functions, which were introduced in 1972 by Bézier [39], are defined as $$J_{n,k}(x) =\sum _{ j=k}^{n}p_{n,j}(x)$$ .

Keywords: Bernstein Basis Functions; Important Research Topics; Baskakov Durrmeyer Operators; Positive Linear Operators; Classical Bernstein Polynomials (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-02765-4_8

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