Classification of Lipschitz Mappings

Abstract

The Lipschitz Condition Nonlinear spectral radius Uniformly lipschitzian mappings Basic Facts on Banach Spaces Convexity The operator norm Dual spaces, reexivity, the weak, and weak* topologies Mean Lipschitz Condition Nonexpansive and mean nonexpansive mappings in Banach spaces General case On the Lipschitz Constants for Iterates of Mean Lipschitzian Mappings A bound for Lipschitz constants of iterates A bound for the constant k (T) Moving averages in Banach spaces A bound for the constant k0(T) More about k(Tn), k0(T), and k (T) Subclasses Determined by p-Averages Basic definitions and observations A bound for k(Tn), k (T), and k0(T) On the moving p-averages Mean Contractions Classical Banach's contractions On characterizations of contractions On the rate of convergence of iterates Nonexpansive Mappings in Banach Space The asymptotic center technique Minimal invariant sets and normal structure Uniformly nonsquare, uniformly noncreasy, and reflexive Banach spaces Remarks on the stability of f.p.p. The case of l1 Mean Nonexpansive Mappings Some new results of stability type Sequential approximation of fixed points The case of n = 3 On the structure of the fixed points set Mean Lipschitzian Mappings with k > 1 Losing compactness in Brouwer's Fixed Point Theorem Retracting onto balls in Banach spaces Minimal displacement Optimal retractions Generalized characteristics of minimal displacement Bibliography Index