Demyanov Difference in Infinite-Dimensional Spaces
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.
KeywordsMinkowski subtraction Demyanov difference Pairs of closed bounded convex sets
- Pontryagin L.S.: On linear differential games II (Russian). Dokl. Acad. Nauk SSSR 175, 764–766 (1967)Google Scholar