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OverviewThis 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. Full Product DetailsAuthor: Vittorino PataPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2019 Volume: 116 Weight: 0.454kg ISBN: 9783030196691ISBN 10: 3030196690 Pages: 171 Publication Date: 01 July 2019 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 The Banach contraction principle 7.- 2 The Boyd-Wongtheorem 13.- 3 Further extensions of the contraction principle 16.- 4 Weak contractions 23.- 5 Contractions of ε-type 29.- 6 Sequences of maps and fixed points 36.- 7 Fixed points of non-expansive maps 39.- 8 The Riesz mean ergodic theorem 42.- 9 The Brouwer fixed point theorem 46.- 10 The Schauder-Tychonoff fixed point theorem 50.- 11 Further consequences of the Schauder-Tychonoff theorem 55.- 12 TheMarkov-Kakutani theorem 60.- 13 TheKakutani-Ky Fan theorem 62.- 14 The implicit function theorem 70.- 15 Location of zeros 75.- 16 Ordinary differential equations in Banach spaces 78.- 17 The Lax-Milgram lemma 89.- 18 An abstract elliptic problem 97.- 19 Semilinear evolution equations 101.- 20 An abstract parabolic problem 108.- 21 The invariant subspace problem 114.- 22 Measure preserving maps on compact Hausdorff spaces 118.- 23 Invariant means on semigroups 120.- 24 Haar measures 123.- 25 Game theory 130.- 26 Problems.ReviewsIt could be used as a textbook for a somewhat unusual functional analysis course, or for a real analysis course that 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) This book is certainly one of the best. It should be quite useful to anybody interested in the theory, methods, and applications of nonlinear functional analysis, in particular to students during their masters studies (il maledetto 3+2, una grossa sciocchezza politica che fa soffrire tanti studenti). (Jurgen Appell, zbMATH 1448.47001, 2020) 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 course that 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) “This book is certainly one of the best. It should be quite useful to anybody interested in the theory, methods, and applications of nonlinear functional analysis, in particular to students during their masters studies (il maledetto 3+2, una grossa sciocchezza politica che fa soffrire tanti studenti).” (Jürgen Appell, zbMATH 1448.47001, 2020) “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 course that 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) Author InformationVittorino Pata completed his PhD in Pure Mathematics at Indiana University, USA in December 1994. Since 2000, he has been a Professor of Mathematical Analysis at the Politecnico di Milano, Italy. His research interests touch several areas of pure and applied mathematics, including ordinary and partial differential equations (with particular emphasis on the asymptotic behavior of solutions), infinite-dimensional dynamical systems, real and functional analysis, operator theory, and noncommutative probability. Tab Content 6Author Website:Countries AvailableAll regions |
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