2004/08/24 by Tomonari Suzuki, Suzuki, Tomonari
Computer Science · Mathematics · #47H10 #47H20 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:47H10 #msc:47H20
paper · pdf · doi:10.48550/arxiv.math/0408329
10 pages
arxiv created 2004/08/24 · openalex publication_date 2004/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove the following theorem: Let T(t) : t >= 0 be a one-parameter continuous semigroup of mappings on a subset C of a Banach space E. The set of fixed points of T(t) is denoted by F(T(t)) for each t >= 0. Then capt >= 0 F(T(t)) = F(T(1)) cap F(T(sqrt 2)) holds. Using this theorem, we discuss convergence theorems to a common fixed point of T(t) : t >= 0.