Convexity-preserving properties of set-valued ratios of affine functions
DOI:
https://doi.org/10.24193/subbmath.2021.3.14Keywords:
Set-valued affine function, single-valued selection, ratio of affine functions, generalized convexity.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 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.
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