  The purpose of this paper is to show stability of order preserving/reversing
transforms on the class of non-negative convex functions in ${\mathbb R}^n$,
and its subclass, the class of non-negative convex functions attaining $0$ at
the origin (these are called "geometric convex functions"). We show that
transforms that satisfy conditions which are weaker than order preserving
transforms, are essentially close to the order preserving transforms on the
mentioned structures.
