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

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 $\left| {f(x)} \right| \leqslant 2{\text{ }}\mathop {{\text{sup}}}\limits_{x,x + kh \in [0,1]} {\text{ }}\left| {\sum\limits_{j = 0}^k {( - 1)^j } \left( {\mathop {}\limits_j^k } \right)f(x + jh)} \right|.$