2024/03/05 by Alona Mokhov, Mokhov, Alona, Nira Dyn +3
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2403.02858
openalex publication_date 2024/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically differentiable set-valued function at a point is defined and studied. This local approximant may be regarded as a special realization of the set-valued Euler approximants of M.~S.~Nikolskii and the directives of Z.~Artstein. Error estimates for the local metric linear approximant are obtained. In particular, second order approximation is derived for a class of ``strongly'' metrically differentiable set-valued maps.