Convexity-preserving properties of set-valued ratios of affine functions - ORZAN, Alexandru; POPOVICI, Nicolae (Studia Universitatis Babeș-Bolyai Mathematica, 2021)
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 affine functions represent such a class. To this aim, we characterize them in terms of vector-valued selections that are ratios of affine functions in the classical sense of Rothblum. Mathematics Subject Classification (2010): 54C60, 26B25.