Fixed Point Theorems and Applications

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 map...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Pata, Vittorino (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
Έκδοση:1st ed. 2019.
Σειρά:La Matematica per il 3+2, 116
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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245 1 0 |a Fixed Point Theorems and Applications  |h [electronic resource] /  |c by Vittorino Pata. 
250 |a 1st ed. 2019. 
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300 |a XVII, 171 p. 1 illus.  |b online resource. 
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490 1 |a La Matematica per il 3+2,  |x 2038-5722 ;  |v 116 
505 0 |a 1 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. 
520 |a 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. 
650 0 |a Functional analysis. 
650 0 |a Partial differential equations. 
650 0 |a Differential equations. 
650 0 |a Topology. 
650 1 4 |a Functional Analysis.  |0 http://scigraph.springernature.com/things/product-market-codes/M12066 
650 2 4 |a Partial Differential Equations.  |0 http://scigraph.springernature.com/things/product-market-codes/M12155 
650 2 4 |a Ordinary Differential Equations.  |0 http://scigraph.springernature.com/things/product-market-codes/M12147 
650 2 4 |a Topology.  |0 http://scigraph.springernature.com/things/product-market-codes/M28000 
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776 0 8 |i Printed edition:  |z 9783030196691 
776 0 8 |i Printed edition:  |z 9783030196714 
830 0 |a La Matematica per il 3+2,  |x 2038-5722 ;  |v 116 
856 4 0 |u https://doi.org/10.1007/978-3-030-19670-7  |z Full Text via HEAL-Link 
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950 |a Mathematics and Statistics (Springer-11649)