2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110217We study a continuous family of norm-preserving isometries of the p-adic unit disk, given as interpolations of a common arithmetic function, the q-analog of the identity, for principal p-adic units q. We show that the fixed point set is trivial except when p=3 and q is a generator of the principal 3-adic units; in that case the isometry given by each q has a unique nontrivial 3-adic fixed point, varying homeomorphically with q.25 pagesNumber Theory11K41 (Primary) 11K55, 11N25, 11S25 (Secondary)text