Demyanov Difference in Infinite-Dimensional Spaces

  • Jerzy Grzybowski
  • Diethard Pallaschke
  • Ryszard Urbański
Part of the Springer Optimization and Its Applications book series (SOIA, volume 87)


In this paper we generalize the Demyanov difference to the case of real Hausdorff topological vector spaces. We prove some classical properties of the Demyanov difference. In the proofs we use a new technique which is based on the properties given in Lemma 1. Due to its importance it will be called the preparation lemma. Moreover, we give connections between Minkowski subtraction and the union of upper differences. We show that in the case of normed spaces the Demyanov difference coincides with classical definitions of Demyanov subtraction.


Minkowski subtraction Demyanov difference Pairs of closed bounded convex sets 


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jerzy Grzybowski
    • 1
  • Diethard Pallaschke
    • 2
  • Ryszard Urbański
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland
  2. 2.Institute of Operations ResearchUniversity of Karlsruhe (KIT)KarlsruheGermany

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