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The Limiting Semigroup of the Genuine Bernstein–Durrmeyer Iterates

✍ Scribed by Daniela Kacsó

Publisher
Springer
Year
2009
Tongue
English
Weight
431 KB
Volume
53
Category
Article
ISSN
1422-6383

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The linear combination of iterates \(1-\left(1-P_{n}\right)^{M}\) of Bernstein and Durrmeyer operators of a fixed degree \(n\) is considered for increasing order of iteration \(M\). The resulting sequence of polynomials is shown to converge to the Lagrange interpolating polynomial for the Bernstein

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In this paper, we establish two basic functional-type identities between the iterates of the Bleimann᎐Butzer᎐Hahn operator and those of the Bernstein Ž . operator, on the one hand, and the iterates of the modified Meyer᎐Konig and Zeller operator and those of the Baskakov operator, on the other. Thes