2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164457Utilizing our recent proximal-average based results on the constructive extension of monotone operators, we provide a novel approach to the celebrated Kirszbraun-Valentine Theorem and to the extension of firmly nonexpansive mappings.Functional AnalysisOptimization and Control46C05; 47H09; 52A41; 90C25Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theorytext