2013/04/29 by Michel Théra, Van Ngai, Huynh, Théra, Michel A.
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Equations Stability Results #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.1304.7748
openalex publication_date 2013/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by using the relative lower semicontinuous envelopes of the distance functions to set-valued mappings. We then apply these characterizations to establish a coderivative type criterion for directional metric regularity as well as for the robustness of metric regularity.