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

Alexandru Orzan, Nicolae Popovici


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.


Set-valued affine function; single-valued selection; ratio of affine functions; generalized convexity.

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