English

Some remarks on contractive and existence sets

Functional Analysis 2021-12-02 v1

Abstract

Let X be a real or complex Banach space and let F in X be a non-empty set. F is called an existence set of best coapproximation (existence set for brevity), if for any x in X, RF(x)R_F(x) is not the empty set, where RF(x)={dF:dcxc for any cF}. R_F (x) = \{ d \in F : \|d-c\| \leq \|x-c\| \hbox{ for any } c \in 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.

Cite

@article{arxiv.2112.00366,
  title  = {Some remarks on contractive and existence sets},
  author = {Maciej Ciesielski and Grzegorz Lewicki},
  journal= {arXiv preprint arXiv:2112.00366},
  year   = {2021}
}
R2 v1 2026-06-24T07:59:19.635Z