A Refinement of Schwarz–Pick Lemma for Higher Derivatives

In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita