2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139686We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.11 pages, v2 references added, v3 a proof modifiedComplex Variables32Q45; 32A25; 52A20text