Classification of Lipschitz Mappings

This book presents a systematic, self-contained treatment of a new, more precise classification of Lipschitz mappings and its application in many topics of metric fixed point theory. The mean Lipschitz condition introduced by Goebel, Japón Pineda, and Sims is relatively easy to check and turns out to satisfy several principles: regulating the possible growth of the sequence of Lipschitz constants k(Tn), ensuring good estimates for k0(T) and k¿(T), and providing some new results in metric fixed point theory.

List of contents

The Lipschitz Condition. Basic Facts on Banach Spaces. Mean Lipschitz Condition. On the Lipschitz Constants for Iterates of Mean Lipschitzian Mappings. Subclasses Determined by p-Averages. Mean Contractions. Nonexpansive Mappings in Banach Space. Mean Nonexpansive Mappings. Mean Lipschitzian Mappings with k > 1. Bibliography. Index.

About the author

Piasecki, ¿ukasz

Summary

Classification of Lipschitz Mappings presents a systematic, self-contained treatment of a new classification of Lipschitz mappings and its application in many topics of metric fixed point theory. Suitable for readers interested in metric fixed point theory, differential equations, and dynamical systems, the book only requires a basic background in functional analysis and topology.

The author focuses on a more precise classification of Lipschitzian mappings. The mean Lipschitz condition introduced by Goebel, Japón Pineda, and Sims is relatively easy to check and turns out to satisfy several principles:

• Regulating the possible growth of the sequence of Lipschitz constants k(Tn)



• Ensuring good estimates for k0(T) and k∞(T)



• Providing some new results in metric fixed point theory

Product details

• Authors: ?Ukasz Piasecki, ¿Ukasz Piasecki, Lukasz Piasecki, Łukasz Piasecki, Lukasz (Instytut Matematyki Piasecki
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Paperback / Softback
• Released: 31.08.2019
• EAN: 9780367379049
• ISBN: 978-0-367-37904-9
• No. of pages: 234
• Series: Chapman & Hall/CRC Pure and Applied Mathematics; Chapman & Hall/CRC Pure and Applied Mathematics; Chapman & Hall/CRC Monographs and Research Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > General, dictionaries; MATHEMATICS / Differential Equations / General, Differential calculus & equations, Differential calculus and equations