Demyanov Difference in Infinite-Dimensional Spaces

Jerzy Grzybowski (), Diethard Pallaschke () and Ryszard Urbański ()
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Jerzy Grzybowski: Adam Mickiewicz University
Diethard Pallaschke: University of Karlsruhe (KIT)
Ryszard Urbański: Adam Mickiewicz University

A chapter in Constructive Nonsmooth Analysis and Related Topics, 2014, pp 13-24 from Springer

Abstract: Abstract 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.

Keywords: Minkowski subtraction; Demyanov difference; Pairs of closed bounded convex sets (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-8615-2_2

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DOI: 10.1007/978-1-4614-8615-2_2

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