The degree of approximation of differentiable functions by Hermite interpolation polynomials (Q1187283)

Let \(f\in C^ p_{\langle-1,1\rangle}\) and \(L_{p,n}[f]\) be an Hermite interpolatory polynomial of degree \([n(p+1)-1]\). The author proves that \[ \| f-L_{p,n}[f]\|=O(1)\{\log(n)\}n^{- p}\omega(f^{(p)};n^{-1}), \] where \(\|\cdot\|\) is the maximum norm on \(\langle-1,1\rangle\) and \(\omega(f,t)\) is the modulus of continuity of \(f\).