Complex mean-value interpolation and approximation of holomorphic functions

We show that complex mean-value interpolation, a generalization of Lagrange-Hermite interpolation, may be defined in any domain that is C-convex, whereas the original definition required ordinary, real convexity. We also show that C-convex domains are the natural ones in which to perform mean-value interpolation, in the sense that any Runge domain which admits mean-value interpolation must in fact be C-convex. Finally, we obtain an integral formula for the error and give some applications concerning approximation of holomorphic functions. (C) 1997 Academic Press.