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.
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Communicated by Tim N.T. Goodman.
In memory of Jean Favard (1902–1965), a great mathematician and human being.
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Abel, U., Butzer, P.L. Complete Asymptotic Expansion for Generalized Favard Operators. Constr Approx 35, 73–88 (2012). https://doi.org/10.1007/s00365-011-9134-y
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DOI: https://doi.org/10.1007/s00365-011-9134-y
Keywords
- Approximation by positive operators
- Rate of convergence
- Degree of approximation
- Simultaneous approximation
- Asymptotic expansions