Abstract:
This paper is devoted to an application of the methods of geometric function theory of a single complex variable and some results from the theory of conformal and quasiconformal mappings to a solution of the direct problem of the constructive theory of functions.
Direct theorems are obtained for the theory of approximation of functions regular in regions bounded by quasiconformal curves admitting a geometric description. In particular, direct theorems are obtained for arbitrary bounded convex regions.