A SHARP SCHWARZ AND CARATHÉODORY INEQUALITY ON THE BOUNDARY Ornek, Bulent Nafi;
In this paper, a boundary version of the Schwarz and Carathodory inequality are investigated. New inequalities of the Carathodory's inequality and Schwarz lemma at boundary are obtained by taking into account zeros of f(z) function which are different from zero. The sharpness of these inequalities is also proved.
Schwarz lemma on the boundary;holomorphic function;Julia-Wolff-Lemma;
G. Kresin and V. Maz'ya, Sharp Real-Part Theorems: A Unified Approach, Translated from the Russian and edited by T. Shaposhnikova. Lecture Notes in Mathematics, 1903. Springer, Berlin, 2007.
A. I. Markushevich, Theory of Functions of a Complex Variable. Vol. I, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1965.
R. Osserman, A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc. 128 (2000), no. 12, 3513-3517.
Ch. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.