2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119244In the present paper, we introduce a new class of sequences called $NBVS$ to generalize $GBVS$, essentially extending monotonicity from "one sided" to "two sided", while some important classical results keep true.21 papges; Accepted by Acta Math. HungarClassical Analysis and ODEs42A20; 42A32A Generalization of Monotonicity Condition and Applicationstext