Convexity-preserving properties of set-valued ratios of affine functions

Abstract

"The aim of this paper is to introduce some classes of set-valued functions that preserve the convexity of sets by direct and inverse images. In particular, we show that the so-called set-valued ratios of a ne functions represent such a class. To this aim, we characterize them in terms of vector-valued selections that are ratios of a ne functions in the classical sense of Rothblum."