On Vector Functions of Bounded Convexity
نویسنده
چکیده
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 aF 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 As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
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