The authors obtain, among others, the following higher derivative generalization of the Schwarz-Pick inequality for analytic self maps on the unit disc of the complex plane. For ,
The proof is obtained by induction using the Faà di Bruno’s formula, as a consequence of recent characterizations of boundedness and compactness of weighted composition operators between Bloch-type spaces due to Ohno, Stroethoff and Zhao. Related work on weighted composition operators on weighted Bloch spaces is due to [M. Contreras and A. G. Hernández-Díaz, J. Aust. Math. Soc., Ser. A 69, 41-60 (2000; Zbl 0990.47018)].