2023/11/02 by Jinlu Li, Li, Jinlu
Computer Science · Mathematics · #26A24 #47A58 #47J30 #49J40 #49J50 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2311.01561
openalex publication_date 2023/11/02 · openalex created_date 2023/11/07 · openalex updated_date 2026/07/28
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X. In this paper, we consider the generalized metric projection operator from X to C, which was introduced by Alber in 1996. We define the Gateaux directional differentiability and investigate some properties of the directional differentiability of the generalized metric projection. In particular, if C is a closed ball, or a closed and convex cone (including proper closed subspaces), or a closed and convex cylinder, then, we give the exact representations of the directional derivatives of the generalized metric projection. We also compare the differences of the directional differentiability between the generalized metric projection and the (standard) metric projection.