A generic result concerning univalent universal functions

摘要

Let $ Omega $ be a Jordan region. We prove that generically every function $ f in H(Omega) $ , univalent in $ Omega $ and continuous on $ overlineOmega $ is universal under derivatives and universal in respect to overconvergence. In fact f realizes both approximations with the same approximative sequence. The proof is based on a modified version of the classical result of J. Walsh concerning approximation of holomorphic functions by polynomials.