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

#### Abstract

The aim of this paper is to introduce some special 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 belong to these classes, by characterizing them in terms of vector-valued selections that are ratios of affine functions in the classical sense of Rothblum.

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DOI: http://dx.doi.org/10.24193/subbmath.2021.3.14

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