Some remarks on contractive and existence sets
[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] pracownik
2023
artykuł naukowy
angielski
- Banach spaces
- reflexivity
- strict convexity
- contractive and existence sets
- one complemented spaces
EN Let X be a real or complex Banach space and let F ⊂ X be a non-empty set. F is called an existence set of best coapproximation (existence set for brevity), if for any x ∈ X , R F (x) ≠ ∅, where R F (x) = {d ∈ F : ‖d − c‖ ≤ ‖x − c‖ for any c ∈ F}. It is clear that any existence set is a contractive subset of X . The aim of this paper is to present some conditions on F and X under which the notions of exsistence set and contractive set are equivalent.
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