Simultaneous approximation and interpolation of functions on continua in   the complex plane
  We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, $k \ge 1$) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E. Furthermore, the error in this approximation is decaying as $e^{-cn^\alpha}$ strictly inside E, where c and $\alpha$ are positive constants independent of the degree n of the approximating polynomial. 
V. V. Andrievskii, I. E. Pritsker and R. S. Varga