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El. knyga: Classification of Lipschitz Mappings

(Monmouth University), , (Universidad Veracruzana, Campanario #5B, La Pradera)
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"This book 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"--

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 k8(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


This book 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.

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.

Torrey M. Gallagher is an Assistant Professor of Mathematics at Monmouth University (New Jersey, USA). His research interests include metric fixed point theory, Banach space geometry, and functional analysis.

Vķctor Pérez-Garcķa is a full time professor at Faculty of Mathematics, University of Veracruz, Mexico. Areas of interest: Functional Analysis, Discrete Mathematics.

ukasz Piasecki is an Associate Professor at the Institute of Mathematics at Maria Curie-Sk lodowska University (Lublin, Poland). His research interests include metric fixed point theory and Banach space theory.
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