Hardy–Littlewood–Pólya relation in the best dominated approximation in symmetric spaces
[ 1 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
- symmetric space
- strict K -monotonicity
- K -order continuity
- the best approximant
EN We investigate a correspondence between strict K-monotonicity, K-order continuity and the best dominated approximation problems with respect to the Hardy–Littlewood–Pólya relation ≺. Namely, we study, in terms of an LKM point and a UKM point, a necessary condition for uniqueness of the best dominated approximation under the relation ≺ in a symmetric space E. Next, we characterize a relation between a point of K-order continuity and an existence of a best dominated approximant with respect to ≺. Finally, we present a compete criteria, written in a notion of K-order continuity, under which a closed and K-bounded above subset of a symmetric space E is proximinal.
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