Description
This book is a comprehensive guide to fixed point theory, covering the basics of Banach's contraction theorem and various techniques for establishing fixed point results. It also explores the application of fixed point theory in different areas of analysis and discusses its relationship with degree theory. The book is suitable for researchers and graduate students in applicable analysis, with a large bibliography and exercises for further study. It is considered a valuable reference work in the field.
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. Review: '... can be considered as a handbook containing an introduction from the metric and topological fixed-point theory.' Lech Gorniewicz, Zentralblatt fur Mathematik 'n++ can be considered as a handbook containing an introduction from the metric and topological fixed-point theory.' Lech Gorniewicz, Zentralblatt fn++ athematik ?????? can be considered as a handbook containing an introduction from the metric and topological fixed-point theory.??? Lech Gorniewicz, Zentralblatt f??r Mathematik
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