AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY

Abstract

In this paper, a boundary version of the Schwarz lemma for the holomrophic function satisfying f (a) = b, vertical bar a vertical bar < 1, b is an element of C and Rf (z) > alpha, 0 <= alpha < vertical bar b vertical bar for vertical bar z vertical bar < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with Rf(c) = alpha. The sharpness of these inequalities is also proved.