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Hermite–Fejér interpolation operator and characterization of functions
Author(s) -
Xie Tingfan,
Zhou Xinlong
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510704
Subject(s) - mathematics , hermite polynomials , operator (biology) , hermite interpolation , interpolation (computer graphics) , characterization (materials science) , term (time) , shift operator , function (biology) , pure mathematics , mathematical analysis , compact operator , extension (predicate logic) , repressor , chemistry , computer science , biochemistry , quantum mechanics , transcription factor , animation , physics , gene , nanotechnology , biology , evolutionary biology , programming language , materials science , computer graphics (images)
In this paper we investigate the approximation behaviour of the so‐called Hermite–Fejér interpolation operator based on the zeros of Jacobi polynomials. As a result we obtain the asymptotic formula of approximation rate for these operators. Moreover, such a formula is valid for any individual continuous function. We will also study the K ‐functional deduced by this operator. Consequently the asymptotic term of this K ‐functional is established. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)