A Generalization of Durrmeyer-Type Polynomials and their Approximation Properties

Octavian Agratini

A chapter in Applications of Fibonacci Numbers, 2004, pp 9-18 from Springer

Abstract: Abstract The Bernstein polynomial approximation process of discrete type defined for every function f belonging to the space C([0, 1]) by $$\left( {{B_n}f} \right)\left( x \right) = \sum\nolimits_{k = 0}^n {{p_{n,k}}} \left( x \right)f\left( {k/n} \right)$$ , where (1) $${p_{n,k}}\left( x \right) = \left( {\frac{n}{k}} \right){x^k}{\left( {1 - x} \right)^{n - k}},x \in [0,1],$$ has been the object of many investigations serving as a guide for theorems that can be proved for a large class of positive linear approximation processes on a bounded interval.

Keywords: 41A10; 41A35; 26D15 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-306-48517-6_2

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