The simultaneous approximation order by Hermite interpolation in a smooth domain (Q1565978)

Let \(D\) be a smooth domain in the complex plane. This paper discusses the simultaneous approximation to a function and its \(i\)th (\(0<i\leq q\)) derivatives by Hermite interpolation on \(D\). The orders of uniform approximation and mean approximation are obtained under some domain boundary conditions. Some known results are included as paticular cases of the theorems of this paper.