Fixed Point Theorems and Applications / by Vittorino Pata.

Format:

Book

Author/Creator:

Pata, Vittorino, 1966- author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Unitext. Matematica per il 3+2 2038-5722 ; 116.

La Matematica per il 3+2, 2038-5722 ; 116

Language:

English

Subjects (All):

Functional analysis.

Differential equations, Partial.

Differential equations.

Topology.

Functional Analysis.

Partial Differential Equations.

Ordinary Differential Equations.

Local Subjects:

Functional Analysis.

Partial Differential Equations.

Ordinary Differential Equations.

Topology.

Physical Description:

1 online resource (XVII, 171 pages) : 1 illustrations.

Edition:

First edition 2019.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

978-3-030-19670-7

9783030196707

OCLC:

1121076109

Access Restriction:

Restricted for use by site license.