Simultaneous approximation and interpolation of functions on continua in the complex plane

We construct polynomial approximations of Dzjadyk type (in terms of the k-t h modulus of continuity, k greater than or equal to 1) for analytic functio ns defined on a continuum E in the complex plane, which simultaneously inte rpolate 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. (C) 2001 Editions scientifiques et medicales Elsevier SAS.