Handbook of metric fixed point theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 703 S. |
| ISBN: | 0792370732 |
Internformat
MARC
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| 245 | 1 | 0 | |a Handbook of metric fixed point theory |c ed. by William A. Kirk ... |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 2001 | |
| 300 | |a XIII, 703 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Fixed point theory | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009556442 | ||
Datensatz im Suchindex
| _version_ | 1804128813060194304 |
|---|---|
| adam_text | Contents
Preface xi
1
Contraction mappings and extensions
W. A. Kirk
1.1 Introduction 1
1.2 The contraction mapping principle 3
1.3 Further extensions of Banach s principle 7
1.4 Caristi s theorem 14
1.5 Set valued contractions 15
1.6 Generalized contractions 18
1.7 Probabilistic metrics and fuzzy sets 20
1.8 Converses to the contraction principle 23
1.9 Notes and remarks 25
2
35
Examples of fixed point free mappings
B. Sims
2.1 Introduction 35
2.2 Examples on closed bounded convex sets 36
2.3 Examples on weak* compact convex sets 40
2.4 Examples on weak compact convex sets 43
2.5 Notes and remarks 47
3
49
Classical theory of nonexpansive mappings
K. Goebel and W. A. Kirk
3.1 Introduction 49
3.2 Classical existence results 50
3.3 Properties of the fixed point set 64
3.4 Approximation 69
3.5 Set valued nonexpansive mappings 78
v
vi
3.6 Abstract theory 79
4
93
Geometrical background of metric fixed point theory
5. Prus
4.1 Introduction 93
4.2 Strict convexity and smoothness 93
4.3 Finite dimensional uniform convexity and smoothness 98
4.4 Infinite dimensional geometrical properties 108
4.5 Normal structure 118
4.6 Bibliographic notes 127
5
133
Some moduli and constants related to metric fixed point theory
E. L. Fuster
5.1 Introduction 133
5.2 Moduli and related properties 134
5.3 List of coefficients 157
6
177
Ultra methods in metric fixed point theory
M. A. Khamsi and B. Sims
6.1 Introduction 177
6.2 Ultrapowers of Banach spaces 177
6.3 Fixed point theory 186
6.4 Maurey s fundamental theorems 193
6.5 Lin s results 195
6.6 Notes and remarks 197
7
201
Stability of the fixed point property for nonexpansive mappings
J. Garcia Falset, A. Jimenez Melado and E. Llorens Fuster
7.1 Introduction 201
7.2 Stability of normal structure 204
7.3 Stability for weakly orthogonal Banach lattices 212
7.4 Stability of the property M(X) 1 217
7.5 Stability for Hilbert spaces. Lin s theorem 223
7.6 Stability for the t FPP 228
7.7 Further remarks 231
7.8 Summary 236
Contents vii
8
239
Metric fixed point results concerning measures of noncompactness
T. Dominguez, M. A. Japon and G. Lopez
8.1 Preface 239
8.2 Kuratowski and Hausdorff measures of noncompactness 240
8.3 0 minimal sets and the separation measure of noncompactness 244
8.4 Moduli of noncompact convexity 248
8.5 Fixed point theorems derived from normal structure 252
8.6 Fixed points in NUS spaces 257
8.7 Asymptotically regular mappings 260
8.8 Comments and further results in this chapter 264
9
, 269
Renormings of £ and Co and fixed point properties
P. N. Dowling, C. J. Lennard and B. Turett
9.1 Preliminaries 269
9.2 Renormings of (} and Co and fixed point properties 271
9.3 Notes and remarks 294
10
299
Nonexpansive mappings: boundary/inwardness conditions and local theory
W. A. Kirk and C. H. Morales
10.1 Inwardness conditions 299
10.2 Boundary conditions 301
10.3 Locally nonexpansive mappings 308
10.4 Locally pseudocontractive mappings 310
10.5 Remarks 320
11
323
Rotative mappings and mappings with constant displacement
W. Kaczor and M. Koter Morgowska
11.1 Introduction 323
11.2 Rotative mappings 323
11.3 Firmly lipschitzian mappings 330
11.4 Mappings with constant displacement 333
11.5 Notes and remarks 336
12
339
Geometric properties related to fixed point theory in some Banach function lattices
S. Chen, Y. Cui, H. Hudzik and B. Sims
12.1 Introduction 339
viii
12.2 Normal structure, weak normal structure, weak sum property, sum property
and uniform normal structure 343
12.3 Uniform rotundity in every direction 356
12.4 B convexity and uniform monotonicity 358
12.5 Nearly uniform convexity and nearly uniform smoothness 362
12.6 WORTH and uniform nonsquareness 367
12.7 Opial property and uniform opial property in modular sequence spaces 368
12.8 Garcia Falset coefficient 377
12.9 Cesaro sequence spaces 378
12.10 WCSC, uniform opial property, fc NUC and UNS for cesp 380
13
391
Introduction to hyperconvex spaces
R. Espinola and M. A. Khamsi
13.1 Preface 391
13.2 Introduction and basic definitions 393
13.3 Some basic properties of hyperconvex spaces 394
13.4 Hyperconvexity, injectivity and retraction 399
13.5 More on hyperconvex spaces 405
13.6 Fixed point property and hyperconvexity 411
13.7 Topological fixed point theorems and hyperconvexity 415
13.8 Isbell s hyperconvex hull 418
13.9 Set valued mappings in hyperconvex spaces 422
13.10 The KKM theory in hyperconvex spaces 428
13.11 Lambda hyperconvexity 431
14
437
Fixed points of holomorphic mappings: a metric approach
T. Kuczumow, S. Reich and D. Shoikhet
14.1 Introduction 437
14.2 Preliminaries 438
14.3 The Kobayashi distance on bounded convex domains 440
14.4 The Kobayashi distance on the Hilbert ball 447
14.5 Fixed points in Banach spaces 450
14.6 Fixed points in the Hilbert ball 454
14.7 Fixed points in finite powers of the Hilbert ball 460
14.8 Isometries on the Hilbert ball and its finite powers 465
14.9 The extension problem 469
14.10 Approximating sequences in the Hilbert ball 472
14.11 Fixed points in infinite powers of the Hilbert ball 481
14.12 The Denjoy Wolff theorem in the Hilbert ball and its powers 483
14.13 The Denjoy WolfF theorem in Banach spaces 490
Contents ix
14.14 Retractions onto fixed point sets 496
14.15 Fixed points of continuous semigroups 502
14.16 Final notes and remarks 507
15
Fixed point and non linear ergodic theorems for semigroups of non linear mappings
A. Lau and W. Takahashi
15.1 Introduction 517
15.2 Some preliminaries 518
15.3 Submean and reversibility 519
15.4 Submean and normal structure 523
15.5 Fixed point theorem 527
15.6 Fixed point sets and left ideal orbits 532
15.7 Ergodic theorems 538
15.8 Related results 545
16
Generic aspects of metric fixed point theory
5. Reich and A. J. Zaslavski
16.1 Introduction 557
16.2 Hyperbolic spaces 557
16.3 Successive approximations 558
16.4 Contractive mappings 561
16.5 Infinite products 564
16.6 (i^) attracting mappings 567
16.7 Contractive set valued mappings 568
16.8 Nonexpansive set valued mappings 569
16.9 Porosity 570
17
Metric environment of the topological fixed point theorems
K. Goebel
17.1 Introduction 577
17.2 Schauder s theorem 579
17.3 Minimal displacement problem 586
17.4 Optimal retraction problem 597
17.5 The case of Hilbert space 604
17.6 Notes and remarks 608
18
613
Order theoretic aspects of metric fixed point theory
X
J. Jachymski
18.1 Introduction 613
18.2 The Knaster Tarski theorem 614
18.3 Zermelo s fixed point theorem 623
18.4 The Tarski Kantorovitch theorem 630
19
643
Fixed point and related theorems for set valued mappings
G. Yuan
19.1 Introduction 643
19.2 Knaster Kuratowski Mazurkiewicz principle 644
19.3 Ky Fan minimax principle 651
19.4 Ky Fan minimax inequality I 653
19.5 Ky Fan minimax inequality II 659
19.6 Fan Glicksberg fixed points in G convex spaces 662
19.7 Nonlinear analysis of hyperconvex metric spaces 666
Index 691
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| language | English |
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| spelling | Handbook of metric fixed point theory ed. by William A. Kirk ... Dordrecht [u.a.] Kluwer Acad. Publ. 2001 XIII, 703 S. txt rdacontent n rdamedia nc rdacarrier Fixed point theory Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Fixpunkttheorie (DE-588)4293945-8 s Metrischer Raum (DE-588)4169745-5 s DE-604 Kirk, William A. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009556442&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handbook of metric fixed point theory Fixed point theory Fixpunkttheorie (DE-588)4293945-8 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4293945-8 (DE-588)4169745-5 (DE-588)4143413-4 |
| title | Handbook of metric fixed point theory |
| title_auth | Handbook of metric fixed point theory |
| title_exact_search | Handbook of metric fixed point theory |
| title_full | Handbook of metric fixed point theory ed. by William A. Kirk ... |
| title_fullStr | Handbook of metric fixed point theory ed. by William A. Kirk ... |
| title_full_unstemmed | Handbook of metric fixed point theory ed. by William A. Kirk ... |
| title_short | Handbook of metric fixed point theory |
| title_sort | handbook of metric fixed point theory |
| topic | Fixed point theory Fixpunkttheorie (DE-588)4293945-8 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Fixed point theory Fixpunkttheorie Metrischer Raum Aufsatzsammlung |
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