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 greater than or equal to 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 e(-cn alpha) strictly inside E, where c and alpha are positive constants independent of the degree n of the as e approximating polynomial