2021/10/26 by Michael Dymond, Dymond, Michael
Computer Science · Mathematics · #47H09 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2110.13722
openalex publication_date 2021/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any non-trivial convex and bounded subset C of a Banach space, we show that outside of a σ-porous subset of the space of non-expansive mappings C→ C, all mappings have the maximal Lipschitz constant one witnessed locally at typical points of C. This extends a result of Bargetz and the author from separable Banach spaces to all Banach spaces and the proof given is completely independent. We further establish a fine relationship between the classes of exceptional sets involved in this statement, captured by the hierarchy of notions of ϕ-porosity.