Nearest point problem in countably normed spaces
Functional Analysis
2022-12-14 v1
Abstract
In a countably normed space which is a linear space equipped with a countable number of pair-wise compatible norms, we prove the existence of a common nearest point (in all norms) from a point outside a nonempty subset if this subset is compact with respect to all norms. We also prove the uniqueness of that common nearest point if the completion of the space equipped with only one of its norms is uniformly convex.
Cite
@article{arxiv.2212.06236,
title = {Nearest point problem in countably normed spaces},
author = {Moustafa M. Zakaria and Nashat Faried and Hany A. El-Sharkawy},
journal= {arXiv preprint arXiv:2212.06236},
year = {2022}
}