2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119246To verify the universal validity of the "two-sided" monotonicity condition introduced in [8], we will apply it to include more classical examples. The present paper selects the $L^{p}$ convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial.10 pagesClassical Analysis and ODEs42A20; 42A32text