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  3. Fixed Point Theory and Applications
  • Cited by 380
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
2001
Online ISBN:
9780511543005
DOI:
https://doi.org/10.1017/CBO9780511543005
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
Cambridge Tracts in Mathematics (141)
Information

Book description

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

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