We consider the multi-point Schwarz-Pick Lemma and its associate functions due to Beardon-Minda and Baribeau-Rivard-Wegert. Basic properties of the associate functions are summarized. Then we observe that special cases of the multi-point Schwarz-Pick Lemma give the Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.
- Dieudonńe's Lemma
- Nevanlinna-Pick interpolation
- Peschl's invariant derivative
- Schur algorithm
- Schwarz-Pick Lemma