Fixed Point Theorems and Applications

• 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: Functional analysis.; Partial differential equations.; Differential equations.; Topology.; Functional Analysis.; Partial Differential Equations.; Ordinary Differential Equations.

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...

Πίνακας περιεχομένων:

• 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.