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Full Description
Classification of Lipschitz Mappings, Second Edition presents a systematic, self-contained treatment of a new classification of Lipschitz mappings and its applications, particularly to metric fixed point theory. Suitable for readers interested in nonlinear analysis, metric fixed point theory, differential equations, ergodic theory, and dynamical systems, the book requires only a basic background in functional analysis and topology, and should therefore be accessible to graduate students or advanced undergraduates, as well as to professionals looking for new topics in metric fixed point theory.
In particular, the second edition contains results related to:
Regulating the growth of the sequence of Lipschitz constants k(Tn)
Ensuring good estimates for k0(T) and k∞(T)
Studying moving harmonic and geometric averages as well as generalized Fibonacci-type sequences and their application to provide a new algorithm for solving polynomials in the real case and in Banach algebras
Classifying mean isometries and mean contractions
Generalizing Browder's famous Demiclosedness Principle
Providing some new results in metric fixed point theory
Minimal displacement and optimal retraction problems
Contents
1. Basic facts about Banach spaces. 2. Mean Lipschitzian Mappings. 3. On the Lipschitz constants for iterates of mean lipschitzian mappings. 4. Some applications. 5. Nonexpansive mappings in Banach spaces. 6. Fixed point property for mean nonexpansive mappings. 7. Mean lipschitzian mappings with k > 1.
