On the interpolation constants of Whitney (Q1358505)

The main result is as follows. Theorem. Let \(f\in C[0,1]\) and \(P\) be an algebraic polynomial of degree \(\leq n-1\) such that \[ f\left ({i\over n-1} \right)= P\left({i \over n-1} \right), \quad i=0,1, \dots, n-1. \] Then \[ \sup_{0\leq x\leq 1} \bigl|f(x)-P(x) \bigr|<5 \sup_{x, x+ nh \in[0,1]} \bigl|\Delta^n_hf(x) \bigr|. \] Here \[ \Delta^n_h f(x): =\sum^n_{j =0} (-1)^j {n\choose j} f(x+jh). \]