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Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7

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Abstract

Let f ∈ C[0, 1], k = 5, 6, 7. We prove that if f(i/(k − 1)) = 0, i = 0, 1,..., k − 1, then \(\left| {f(x)} \right| \leqslant 2{\text{ }}\mathop {{\text{sup}}}\limits_{x,x + kh \in [0,1]} {\text{ }}\left| {\sum\limits_{j = 0}^k {( - 1)^j } \left( {\mathop {}\limits_j^k } \right)f(x + jh)} \right|.\)

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  1. Shevchenko Kiev University, Kiev

    O. D. Zhelnov

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  1. O. D. Zhelnov
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Zhelnov, O.D. Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7. Ukrainian Mathematical Journal 55, 660–664 (2003). https://doi.org/10.1023/B:UKMA.0000010165.32895.99

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  • DOI: https://doi.org/10.1023/B:UKMA.0000010165.32895.99

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