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Results in Mathematics

, Volume 50, Issue 3–4, pp 213–225 | Cite as

On Genuine Bernstein–Durrmeyer Operators

  • Heiner Gonska
  • Daniela Kacsó
  • Ioan Raşa
Article

Abstract.

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U n , compute the moments of T(t) and establish asymptotic formulas.

Mathematics Subject Classification (2000).

41A36 41A25 41A17 41A10 20Mxx 47A75 

Keywords.

Genuine Bernstein–Durrmeyer operators iterates of operators limiting semigroup degree of approximation eigenstructure moments of positive linear operators asymptotic formulas 

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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Duisburg-EssenDuisburgGermany
  2. 2.Department of MathematicsUniversity of BochumBochumGermany
  3. 3.Department of MathematicsTechnical UniversityCluj-NapocaRomania

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