2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68157We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing multilinear mappings coincides with the whole space of continuous multilinear mappings.to appear in Arch. Math. (Basel)Functional Analysistext