Best error bounds for derivatives in two point Birkhoff interpolation problems (Q1057434)

Let the real function \(u\in C^{2m}[0,1]\) be given and L be the unique polynomial of degree \(\leq 2m-1\) which interpolates u and its first m-1 even derivatives \(u^{(2j)}\) at 0 and 1. The author gives pointwise bounds of the error u-L and its derivatives in terms of the sup norm of \(u^{(2m)}\) and the Euler polynomials. Further, he proves some particular results on the two point Birkhoff interpolation problems by means of a theorem of Birkhoff and Priver on the same subject.