2019-06-182019-06-182002-08Bernal González, L. y Calderón Moreno, M.d.C. (2002). Two hyperbolic Schwarz lemmas. Bulletin of the Australian Mathematical Society, 66 (1), 17-24.0004-97271755-1633https://hdl.handle.net/11441/87485In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings on the unit disk with fixed multiplicity for the zero at the origin, hence extending a recent result due to Beardon. A property of preserving hyperbolic distances also studied by Beardon is here completely characterized.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Schwarz-Pick LemmaHigher order hyperbolic derivativeHyperbolic distanceMultiplicity at a pointm-automorphism of the unit diskinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1017/S0004972700020633