2022/12/12 by Moustafa M. Zakaria, Zakaria, Moustafa M., Nashat Faried +3
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2212.06236
openalex publication_date 2022/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.