Complex Mean-Value Interpolation and Approximation of Holomorphic Functions Original Research Article

We show that complex mean-value interpolation, a generalizationof Lagrange–Hermite interpolation, may be defined in anydomain that is C-convex, whereas the original definition requiredordinary, real convexity. We also show that C-convex domainsare the natural ones in which to perform mean-value interpolation,in the sense that any Runge domain which admits mean-value interpolationmust in fact be C-convex. Finally, we obtain an integral formulafor the error and give some applications concerning approximationof holomorphic functions.