Estimates for the Bernstein Operators

Radu Păltănea
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Radu Păltănea: Transilvania University, Department of Mathematics

Chapter 4 in Approximation Theory Using Positive Linear Operators, 2004, pp 89-129 from Springer

Abstract: Abstract The Bernstein operators B n , n ∈ ℕ assign to each function F ∈ ℱ[0, 1], the polynomials 4.1 $$ {{B}_{n}}(f,x): = \sum\limits_{{k = 0}}^{n} {{{p}_{{n,k}}}(x) \cdot f\left( {\frac{k}{n}} \right),x \in [0,1],\;where} \;{{p}_{{n,k}}}(x): = \left( {\begin{array}{*{20}{c}} n \\ k \\ \end{array} } \right){{x}^{k}}{{(1 - x)}^{{n - k}}}. $$

Keywords: Good Constant; Linear Positive Operator; Direct Part; Symmetrical Relation; Bernstein Operator (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-1-4612-2058-9_4

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