Let D — {3 e C: I s I < rj. be a set and A{T)} be tions on D. In this paper taking complex algebra R, we an algebra of bounded analytic func- gave the characterization of Schwarz theorem. In tlıe special case r = 1, we obtained the characterization of Schwarz lemjna. Taking a e 7? that satisfies some conditions we gave algebraic characterization of conformal mapping from D to Ü, where U = e C: J ıc j < 1|, and investigate the case r = 1.