Hermite–Fejér interpolation operator and characterization of functions |
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| Authors: | Tingfan Xie Xinlong Zhou |
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| Institution: | 1. Department of Mathematics, China Jiliang University, 310018 Hangzhou, P. R. China;2. Phone: +86 571 86914477, Fax: +86 571 86914435;3. Department of Mathematics, University of Duisburg‐Essen, 47048 Duisburg, Germany |
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| Abstract: | 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) |
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| Keywords: | Asymptotic expression approximation rate Hermite− Fejé r interpolation K ‐functional |
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