in the disk D {Izl < 1}, n >_ 1, we set F(z, f) (1 -Izl2)lf’(z)l/(1 -If(z)12), A la, I/(1 -la01), and T(z) zn(z + A)/(1 + Az). Goluzin’s extension of the Schwarz-Pick inequality is that r(z, f) _< r(Izl, r), z D. We shall further improve Goluzin’s inequality with a complete description on the equality condition. For a holomorphic map from a hyperbolic plane domain into another, one can prove a similar result in terms of the Poincar6 metric.

@inproceedings{YamashitaSchwarzPickI,
title={Schwarz-Pick Inequality},
author={Shinji Yamashita}
}