Classification of Lipschitz Mappings

1st Edition

Łukasz Piasecki

Chapman and Hall/CRC
Published December 12, 2013
Reference - 232 Pages - 30 B/W Illustrations
ISBN 9781466595217 - CAT# K20714
Series: Chapman & Hall/CRC Pure and Applied Mathematics

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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

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