Abstract

In this paper algebraic properties of convex sets are studied. In the first section we present one of our main results which is an algebraic order cancellation law of convex sets. Then we study properties of convex pairs and reduced pairs mainly within the general frame of commutative semigroups which satisfy the order cancellation law.

Author information

Contact details are reproduced from the original publication and may be historical.

Jerzy Grzybowski

Faculty of Mathematics and Computer Science, Adam-Mickiewicz-University, Umultowska 87, 61-614 Poznań, Poland

jgrz@amu.edu.pl

Diethard Pallaschke

Institute of Operations Research, Karlsruhe Institute of Technology, Kaiserstr. 89, 76133 Karlsruhe, Germany

diethard.pallaschke@kit.edu

Hubert Przybycień

Faculty of Mathematics and Computer Science, Adam-Mickiewicz-University, Umultowska 87, 61-614 Poznań, Poland

hubert@amu.edu.pl

R. Urbański

Faculty of Mathematics and Computer Science, Adam-Mickiewicz-University, Umultowska 87, 61-614 Poznań, Poland

rich@amu.edu.pl

Keywords

  • Quasidifferential
  • pairs of bounded closed convex sets
  • order cancellation law
  • minimal pairs
  • reduced pairs

Mathematics Subject Classification

52A07, 52A20, 26A27, 26B25

Suggested citation

J. Grzybowski, D. Pallaschke, H. Przybycień, R. Urbański. “Reduced and Minimally Convex Pairs of Sets.” Journal of Convex Analysis 25 (2018), No. 4, 1319–1334. https://doi.org/10.68381/jca25080

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.