  As 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.
