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    STUDIA MATHEMATICA - Issue no. 3 / 2021  
         
  Article:   CONVEXITY-PRESERVING PROPERTIES OF SET-VALUED RATIOS OF AFFINE FUNCTIONS.

Authors:  ALEXANDRU ORZAN, NICOLAE POPOVICI.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath. 2021.3.14

Published Online: 2021-09-30
Published Print: 2021-09-30
pp. 591-602

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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.

Keywords: Set-valued affine function, single-valued selection, ratio of affine functions, generalized convexity.
 
         
     
         
         
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