2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79493We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work ``New simple infinite-dimensional Lie algebras of characteristic 0.''34pages, Latex; To appear in Journal of AlgebraQuantum Algebratext