Classical theory of nonexpansive mappings. (Q2761628)

This survey presents an overview of the classical theory of nonexpansive mappings, concentrating on the following topics: classical existence results (Goebel-Karlovitz lemma, uniformly Lipschitzian mappings, approximate fixed point property, etc.); structure of the fixed point set (nonexpansive retracts, hereditary fixed point property, pathwise connectedness); approximation of fixed points (asymptotic regularity, strong convergence, weak convergence, asymptotic center technique); abstract metric theory (convexity structures, Khamsi's structure theorem).NEWLINENEWLINE The paper contains an extensive bibliography with 143 references.NEWLINENEWLINEFor the entire collection see [Zbl 0970.54001].