2017
Том 69
№ 9

All Issues

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

Zhelnov O. D.

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Abstract

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

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 4, pp 660-664.

Citation Example: Zhelnov O. D. Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 // Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 546-549.

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