2024/09/06 by Christian Bargetz, Bargetz, Christian, Michael Dymond +3
Computer Science · Mathematics · #Optimization and Variational Analysis #Nonlinear Differential Equations Analysis #Fixed Point Theorems Analysis
paper · pdf · doi:10.48550/arxiv.2409.04292
We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banach spaces with the Radon-Nikodym property and all C(K)-spaces for compact Hausdorff K. We also conclude that the typical, in the sense of Baire category, nonexpansive mapping is close to being extremal.