An introduction to metric spaces and fixed point theory:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Wiley
2001
|
| Schriftenreihe: | Pure and applied mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009550733&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 302 S. |
| ISBN: | 0471418250 |
Internformat
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Datensatz im Suchindex
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| adam_text | AN INTRODUCTION TO METRIC SPACES AND FIXED POINT THEORY MOHAMED A.
KHAMSI WILLIAM A. KIRK UF . T . . -, * .,- N
AWILEY-LNTERSCIENCE PUBLICATION I * V . II ,; ,; L RI [ .-;
JOHN WILEY & SONS, INC. NEW YORK / CKJCJIESTEF^WEI.NRIEJM / BRISBANE /
SINGAPORE / TORONTO CONTENTS PREFACE IX METRIC SPACES INTRODUCTION 3 1.1
THE REAL NUMBERS R 3 1.2 CONTINUOUS MAPPINGS IN E 5 1.3 THE TRIANGLE
INEQUALITY IN E 7 1.4 THE TRIANGLE INEQUALITY IN R * 8 1.5 BROUWER S
FIXED POINT THEOREM 10 EXERCISES 11 METRIC SPACES 13 2.1 THE METRIC
TOPOLOGY 15 2.2 EXAMPLES OF METRIC SPACES 19 2.3 COMPLETENESS 26 2.4
SEPARABILITY AND CONNECTEDNESS 33 2.5 METRIC CONVEXITY AND CONVEXITY
STRUCTURES 35 EXERCISES 38 METRIC CONTRACTION PRINCIPLES 41 3.1 BANACH S
CONTRACTION PRINCIPLE 41 3.2 FURTHER EXTENSIONS OF BANACH S PRINCIPLE 46
3.3 THE CARISTI-EKELAND PRINCIPLE 55 3.4 EQUIVALENTS OF THE
CARISTI-EKELAND PRINCIPLE 58 3.5 SET-VALUED CONTRACTIONS 61 3.6
GENERALIZED CONTRACTIONS 64 EXERCISES 67 HYPERCONVEX SPACES 71 4.1
INTRODUCTION 71 4.2 HYPERCONVEXITY 77 4.3 PROPERTIES OF HYPERCONVEX
SPACES 80 4.4 A FIXED POINT THEOREM 84 VI CONTENTS 4.5 INTERSECTIONS OF
HYPERCONVEX SPACES 87 4.6 APPROXIMATE FIXED POINTS 89 4.7 ISBELL S
HYPERCONVEX HULL 91 EXERCISES 98 5 NORMAL STRUCTURES IN METRIC SPACES
101 5.1 A FIXED POINT THEOREM 101 5.2 STRUCTURE OF THE FIXED POINT SET
103 5.3 UNIFORM NORMAL STRUCTURE 106 5.4 UNIFORM RELATIVE NORMAL
STRUCTURE 110 5.5 QUASI-NORMAL STRUCTURE 112 5.6 STABILITY AND NORMAL
STRUCTURE 115 5.7 ULTRAMETRIC SPACES 116 5.8 FIXED POINT SET
STRUCTURE*SEPARABLE CASE 120 EXERCISES 123 II BANACH SPACES 6 BANACH
SPACES: INTRODUCTION 127 6.1 THE DEFINITION 127 6.2 CONVEXITY 131 6.3 H
REVISITED 132 6.4 THE MODULUS OF CONVEXITY 136 6.5 UNIFORM CONVEXITY OF
THE P SPACES 138 6.6 THE DUAL SPACE: HAHN-BANACH THEOREM 142 6.7 THE
WEAK AND WEAK* TOPOLOGIES 144 6.8 THE SPACES C, CQ, T X AND I^ 146 6.9
SOME MORE GENERAL FACTS 148 6.10 THE SCHUR PROPERTY AND L X 150 6.11
MORE ON SCHAUDER BASES IN BANACH SPACES 154 6.12 UNIFORM CONVEXITY AND
REFLEXIVITY 163 6.13 BANACH LATTICES 165 EXERCISES 168 7 CONTINUOUS
MAPPINGS IN BANACH SPACES 171 7.1 INTRODUCTION 171 7.2 BROUWER S THEOREM
173 7.3 FURTHER COMMENTS ON BROUWER S THEOREM 176 7.4 SCHAUDER S THEOREM
179 7.5 STABILITY OF SCHAUDER S THEOREM 180 7.6 BANACH ALGEBRAS: STONE
WEIERSTRASS THEOREM 182 7.7 LERAY-SCHAUDER DEGREE 183 7.8 CONDENSING
MAPPINGS 187 7.9 CONTINUOUS MAPPINGS IN HYPERCONVEX SPACES 191 EXERCISES
195 CONTENTS VII 8 METRIC FIXED POINT THEORY 197 8.1 CONTRACTION
MAPPINGS 197 8.2 BASIC THEOREMS FOR NONEXPANSIVE MAPPINGS 199 8.3 A
CLOSER LOOK AT I X 205 8.4 STABILITY RESULTS IN ARBITRARY SPACES 207 8.5
THE GOEBEL-KARLOVITZ LEMMA 211 8.6 ORTHOGONAL CONVEXITY 213 8.7
STRUCTURE OF THE FIXED POINT SET 215 8.8 ASYMPTOTICALLY REGULAR MAPPINGS
219 8.9 SET-VALUED MAPPINGS 222 8.10 FIXED POINT THEORY IN BANACH
LATTICES 225 EXERCISES 238 9 BANACH SPACE ULTRAPOWERS 243 9.1 FINITE
REPRESENTABILITY 243 9.2 CONVERGENCE OF ULTRANETS 248 9.3 THE BANACH
SPACE ULTRAPOWER X 249 9.4 SOME PROPERTIES OF X 252 9.5 EXTENDING
MAPPINGS TOX 255 9.6 SOME FIXED POINT THEOREMS 257 9.7 ASYMPTOTICALLY
NONEXPANSIVE MAPPINGS 262 9.8 THE DEMICLOSEDNESS PRINCIPLE 263 9.9
UNIFORMLY NON-CREASY SPACES 264 EXERCISES 270 APPENDIX: SET THEORY 273
A.I MAPPINGS 273 A.2 ORDER RELATIONS AND ZERMELO S THEOREM 274 A.3
ZORN S LEMMA AND THE AXIOM OF CHOICE 275 A.4 NETS AND SUBNETS 277 A.5
TYCHONOFF S THEOREM 278 A.6 CARDINAL NUMBERS 280 A.7 ORDINAL NUMBERS AND
TRANSFINITE INDUCTION 281 A.8 ZERMELO S FIXED POINT THEOREM 284 A.9 A
REMARK ABOUT CONSTRUCTIVE MATHEMATICS 286 EXERCISES 287 BIBLIOGRAPHY 289
INDEX 301
|
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| dewey-search | 514/.32 |
| dewey-sort | 3514 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013955978 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:56:32Z |
| institution | BVB |
| isbn | 0471418250 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009550733 |
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| physical | X, 302 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spellingShingle | Khamsi, Mohamed A. An introduction to metric spaces and fixed point theory Metrischer Raum (DE-588)4169745-5 gnd Fixpunkttheorie (DE-588)4293945-8 gnd |
| subject_GND | (DE-588)4169745-5 (DE-588)4293945-8 |
| title | An introduction to metric spaces and fixed point theory |
| title_auth | An introduction to metric spaces and fixed point theory |
| title_exact_search | An introduction to metric spaces and fixed point theory |
| title_full | An introduction to metric spaces and fixed point theory Mohamed A. Khamsi ; William A. Kirk |
| title_fullStr | An introduction to metric spaces and fixed point theory Mohamed A. Khamsi ; William A. Kirk |
| title_full_unstemmed | An introduction to metric spaces and fixed point theory Mohamed A. Khamsi ; William A. Kirk |
| title_short | An introduction to metric spaces and fixed point theory |
| title_sort | an introduction to metric spaces and fixed point theory |
| topic | Metrischer Raum (DE-588)4169745-5 gnd Fixpunkttheorie (DE-588)4293945-8 gnd |
| topic_facet | Metrischer Raum Fixpunkttheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009550733&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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