ON VECTOR FUNCTIONS OF BOUNDED CONVEXITY

Let X be a normed linear space. We investigate properties of vector functions F : [a,b] -> X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K ba F is equal to the variation of F'(+) on [a, b). As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.