Multipoint Schwarz–Pick Lemma for the Quaternionic Case

Abstract Following ideas by Beardon, Minda and Baribeau, Rivard, Wegert in the context of the complex Schwarz–Pick Lemma, we use iterated hyperbolic difference quotients to prove a quaternionic multipoint Schwarz–Pick Lemma, in the context of the theory of slice regular functions. As applications, we obtain quaternionic Dieudonné and Goluzin estimates. Finally, an algorithm for the construction of (Nevanlinna–Pick) interpolating slice regular functions with real nodes is provided as a byproduct of the quaternionic multipoint Schwarz–Pick Lemma.