2025/11/04 by Evseev, Nikita
Computer Science · Mathematics · #30Lxx #46B25 #46E36 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.2511.02520
openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
It is known that a Lipschitz continuous map from the Euclidean domain to a metric space is metrically differentiable almost everywhere. When the metric space is a Banach space dual to separable, the metric differential has its linear counterpart -- weak* differential. However, for an arbitrary metric or Banach space, a Lipschitz map is not necessarily weak* differentiable. This paper introduces an approach based on a concept of weak weak* derivatives. This framework yields a linear representation for the metric differential, allowing for its calculation as the norm of an associated linear operator.