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Constructive Approximation

, Volume 35, Issue 1, pp 73–88 | Cite as

Complete Asymptotic Expansion for Generalized Favard Operators

  • Ulrich Abel
  • Paul L. ButzerEmail author
Article

Abstract

In the present paper we consider a generalization \(F_{n,\sigma_{n}} \) of the Favard operators and study the local rate of convergence for smooth functions. As a main result we derive the complete asymptotic expansion for the sequence \(( F_{n,\sigma _{n}}f)( x)\) as n tends to infinity. Furthermore, we consider a truncated version of these operators. Finally, all results were proved for simultaneous approximation.

Keywords

Approximation by positive operators Rate of convergence Degree of approximation Simultaneous approximation Asymptotic expansions 

Mathematics Subject Classification (2010)

41A36 41A25 41A28 41A60 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Fachbereich MNDTechnische Hochschule MittelhessenFriedbergGermany
  2. 2.Lehrstuhl A für MathematikRWTH Aachen UniversityAachenGermany

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