2017/07/28 by Carlos Benítez, Carlos Alberto Velasco Benítez, Pedro Martín +4
Engineering · Mathematics · #46B20 (Primary) #46C15 #52A10 #52A21 (Secondary) #Advanced Numerical Analysis Techniques #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Mathematics and Applications #math.FA #msc:46B20 #msc:46C15 #msc:52A10 #msc:52A21
paper · pdf · doi:10.48550/arxiv.1707.09171
12 pages, 2 figures
arxiv created 2017/07/28 · openalex publication_date 2017/07/28 · arxiv updated 2017/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Let X be a real normed space with unit sphere S. We prove that X is an inner product space if and only if there exists a real number ρ=√((1+cos(2kπ)/(2m+1))/2), (k=1,2,… , m ; m=1,2,…), such that every chord of S that supports ρS touches ρS at its middle point. If this condition holds, then every point u∈ S is a vertex of a regular polygon that is inscribed in S and circumscribed about ρS.