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A Bibliography of the Bernstein Power Series Operators of Meyer — König and Zeller and Their Generalizations

  • Chapter
Anniversary Volume on Approximation Theory and Functional Analysis

Abstract

Concerning the approximation of nonperiodic functions by positive linear methods the best-known operators are the Bernstein polynomials*) and the singular integral of Landau -Stieltjes (Landau polynomials). Another positive linear approximation process which is attracting increasing attention was introduced by W. MEYER -KÖNIG and K. ZELLER [2]/[3] in 1959/60; for functions f on [0,1) it was originally defined by

$$ {M_n}\left( {f;x} \right): = {\left( {1 - x} \right)^n}\mathop \sum \limits_{k = 0}^\infty \;\;f\left( {\frac{k}{{k + n}}} \right)\left( {_k^{k + n - 1}} \right){\text{ }}{x^k},\quad n \in {\text{N}} $$
((1))

.

Herrn Professor W. Meyer — König zum 70. Geburtstag am 26. Mai 1982 in Dankbarkeit gewidmet.

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Stark, E.L. (1984). A Bibliography of the Bernstein Power Series Operators of Meyer — König and Zeller and Their Generalizations. In: Butzer, P.L., Stens, R.L., Sz.-Nagy, B. (eds) Anniversary Volume on Approximation Theory and Functional Analysis. ISNM 65: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 65. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5432-0_28

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  • DOI: https://doi.org/10.1007/978-3-0348-5432-0_28

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5434-4

  • Online ISBN: 978-3-0348-5432-0

  • eBook Packages: Springer Book Archive

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