Overview
- Employs a unitary approach to explore a key field of modern mathematics
- Discusses all relevant applications of the theory of fixed points in detail
- Although it covers advanced topics, is highly “user friendly”
- The only book of its kind in the current literature
Part of the book series: UNITEXT (UNITEXT, volume 116)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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Table of contents (26 chapters)
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Fixed Point Theorems
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Some Applications
Keywords
About this book
This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master’s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis.
Reviews
“This is a good reference book on the applications of fixed point theory to other fields in mathematics, optimization theory, economics, engineering, and image science. … I must point out that this book lets researchers get their required knowledge on fixed points in a short time.” (Lai-Jiu Lin, Mathematical Reviews, May, 2020)
“It could be used as a textbook for a somewhat unusual functional analysis course, or for a real analysis coursethat introduces functional analysis. It would also be good preparation for a course in nonlinear partial differential equations or control theory.” (John D. Cook, MAA Reviews, October 6, 2019)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Fixed Point Theorems and Applications
Authors: Vittorino Pata
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-030-19670-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-19669-1Published: 01 July 2019
eBook ISBN: 978-3-030-19670-7Published: 22 September 2019
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: XVII, 171
Number of Illustrations: 1 b/w illustrations
Topics: Functional Analysis, Partial Differential Equations, Ordinary Differential Equations, Topology