2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75191As in Hokusai's series of paintings "Thirty six views of mount Fuji" in which mount Fuji's is sometimes scarcely visible, the central topic of this paper is the geometry of $K$-spaces although in some of the seven views presented $K$-spaces are not easily visible. We study the interplay between the behaviour of approximately convex (and approximately affine) functions on the unit ball of a Banach space and the geometry of Banach K-spaces.2 figuresFunctional Analysis46B20; 52A05; 42A65; 26B25text