Uniform convexity, hyperbolic geometry, and nonexpansive mappings:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1984
|
| Series: | Pure and applied mathematics
83 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 170 S. |
| ISBN: | 0824772237 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS
PREFACE iii
CHAPTER 1 BANACH SPACES
1. Basic Facts 1
2. Uniform Convexity 6
3. Nearest Point Projections 11
4. Asymptotic Centers 18
5. Fixed Points in Uniformly Convex Spaces 22
6. The Fixed Point Property for Nonexpansive Mappings 25
7. Stability 32
8. Uniformly Lipschitzian Mappings 34
9. Accretive Operators 38
10. Periodic Solutions 39
11. Firmly Nonexpansive Mappings 41
12. Approximating Curves 44
13. Nonexpansive Retractions 48
14. The Mean Ergodic Theorem 51
15. Iterations 52
16. Inward Mappings 55
17. The Almost Fixed Point Property for Nonexpansive Mappings 57
vi i
viii CONTENTS
CHAPTER 2 HYPERBOLIC GEOMETRY
1. The Schwarz Lemma 61
2. The Poincare Metric 65
3. Balls in (D,p) 67
4. Metric Lines and p Convexity 68
5. Uniform Convexity of (D,p) 70
6. Nonexpansive Mappings in (D,p) 73
7. Equidistant Sets and Half Spaces 79
8. Isometric Models of (D,p) 83
9. Holomorphic Mappings in Banach Spaces 85
10. The Caratheodory Reiffen Finsler Pseudometric 87
11. Schwarz Pick Systems of Pseudometrics 90
12. Automorphisms and Cartan s Uniqueness Theorem 93
13. A Fixed Point Theorem 96
14. The Automorphisms of the Hilbert Ball 97
15. The Hyperbolic Metric on the Hilbert Ball 98
16. Geodesies and Affine Sets 102
17. p Convexity 103
18. Uniform Convexity of (B,p) 105
19. Nearest Point Projections 108
20. Equidistant Sets and Half Spaces 112
21. Asymptotic Centers 115
22. Nonexpansive Mappings in (B,p) 118
23. Fixed Points 120
24. Approximating Curves 121
25. Invariant Domains 124
26. Localization of Fixed Points 127
27. Firmly Nonexpansive Mappings 129
28. Nonexpansive Retractions 132
29. Fixed Points of Automorphisms 135
30. Iterations 137
31. Equivalent and Nonequivalent Domains 143
32. The Real Hilbert Ball 148
CONTENTS i x
CHAPTER 3 SPHERICAL GEOMETRY
1. The Hilbert Sphere 151
2. Uniform Convexity 153
3. Asymptotic Centers 156
4. Fixed Points 157
REFERENCES 161
INDEX 167
|
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| ctrlnum | (OCoLC)441002766 (DE-599)BVBBV000250969 |
| discipline | Mathematik |
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| id | DE-604.BV000250969 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:06Z |
| institution | BVB |
| isbn | 0824772237 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000151247 |
| oclc_num | 441002766 |
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| physical | IX, 170 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Goebel, Kazimierz Verfasser aut Uniform convexity, hyperbolic geometry, and nonexpansive mappings Kazimierz Goebel ; Simeon Reich New York [u.a.] Dekker 1984 IX, 170 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 83 Holomorphe Abbildung (DE-588)4160471-4 gnd rswk-swf Nichtexpansive Abbildung (DE-588)4245092-5 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 s Nichtexpansive Abbildung (DE-588)4245092-5 s DE-604 Hyperbolische Geometrie (DE-588)4161041-6 s Banach-Raum (DE-588)4004402-6 s Reich, Simeon Verfasser aut Pure and applied mathematics 83 (DE-604)BV000001885 83 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000151247&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goebel, Kazimierz Reich, Simeon Uniform convexity, hyperbolic geometry, and nonexpansive mappings Pure and applied mathematics Holomorphe Abbildung (DE-588)4160471-4 gnd Nichtexpansive Abbildung (DE-588)4245092-5 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4160471-4 (DE-588)4245092-5 (DE-588)4161041-6 (DE-588)4004402-6 |
| title | Uniform convexity, hyperbolic geometry, and nonexpansive mappings |
| title_auth | Uniform convexity, hyperbolic geometry, and nonexpansive mappings |
| title_exact_search | Uniform convexity, hyperbolic geometry, and nonexpansive mappings |
| title_full | Uniform convexity, hyperbolic geometry, and nonexpansive mappings Kazimierz Goebel ; Simeon Reich |
| title_fullStr | Uniform convexity, hyperbolic geometry, and nonexpansive mappings Kazimierz Goebel ; Simeon Reich |
| title_full_unstemmed | Uniform convexity, hyperbolic geometry, and nonexpansive mappings Kazimierz Goebel ; Simeon Reich |
| title_short | Uniform convexity, hyperbolic geometry, and nonexpansive mappings |
| title_sort | uniform convexity hyperbolic geometry and nonexpansive mappings |
| topic | Holomorphe Abbildung (DE-588)4160471-4 gnd Nichtexpansive Abbildung (DE-588)4245092-5 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Holomorphe Abbildung Nichtexpansive Abbildung Hyperbolische Geometrie Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000151247&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
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