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

Author： Zhelnov O. D.  

Publisher： Springer Publishing Company

ISSN： 0041-5995

Source： Ukrainian Mathematical Journal, Vol.55, Iss.4, 2003-04, pp. : 660-664

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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| \le 2 \sup_{x,x+kh \in [0,1]}\left| {\sum_{j=0}^k {(-1)^j{k \choose j} f(x+jh)}} \right|.

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