Topics in nonlinear analysis & applications:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 699 S. |
| ISBN: | 9810225342 |
Internformat
MARC
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| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1997 | |
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Datensatz im Suchindex
| _version_ | 1804126292332773376 |
|---|---|
| adam_text | CONTENTS
Preface IX
CHAPTER 1 1
Cones and Complementarity Problems
1. INTRODUCTION 1
2. CONVEX CONES 2
• Normal cones 4
• Regular and completely regular cones 8
• Well based cones 10
• Isotone projection cones 16
• Galerkin cones 23
3. COMPLEMENTARITY PROBLEMS 27
• The explicit complementarity problem 30
• The implicit complementarity problem 39
• The generalized order complementarity problem 42
4. EXISTENCE THEOREMS 47
• Galerkin cones and the generalized Karamardian condition 47
• Galerkin cones and conically coercive functions 54
• Variational inequalities and explicit complementarity pro¬
blems 59
• Isotone projection cones and complementarity problems 69
• Comment 81
• Complementarity problems and condition (S)+ 82
• S variational inequalities and the implicit complementarity
problem 95
• Heterotonic operators and the generalized order complemen¬
tarity problem 104
• Topological degree and complementarity 117
CONTENTS
5. SOME SPECIAL PROBLEMS IN COMPLEMENTARITY
THEORY 132
• Boundedness of the solution set 132
• Solution which is the least element of the feasible set 135
• The cardinality of the solution set 139
• Nonexistence of solution 139
• Sensitivity analysis 139
• Nonlinear complementarity and quasi equilibria 139
6. COMPLEMENTARITY AND FIXED POINTS 140
7. REFERENCES 148
CHAPTER 2 167
Metrics on Convex Cones
1. INTRODUCTION 167
2. fflLBERT S PROJECTIVE METRIC 170
3. THOMPSON S METRIC 208
4. WORKING WITH TWO CONES 220
5. MONOTONE SEMIGROUPS AND METRICS ON CONES 228
6. REFERENCES 233
CHAPTER 3 241
Zero Epi Mappings
1. INTRODUCTION 241
2. ZERO EPI MAPPINGS ON BOUNDED SETS 243
3. ZERO EPI MAPPINGS ON THE WHOLE SPACE 255
4. ZERO EPI MAPPINGS ON CONES 271
5. ZERO EPI FAMILIES OF MAPPINGS AND OPTIMIZATION 284
6. ZERO EPI MAPPINGS AND COMPLEMENTARITY PROB¬
LEMS 304
7. ZERO EPI MAPPINGS AND k SET CONTRACTION 315
8. REFERENCES 318
VI
CONTENTS
CHAPTER 4 325
Variational Principles
1. INTRODUCTION 325
2. PRELIMINARIES 328
3. CRITICAL POINTS FOR DYNAMICAL SYSTEMS 343
4. VARIANTS OF EKELAND S VARIATIONAL PRINCIPLE 355
5. THE DROP THEOREM 365
6. STRONG FORMS AND GENERALIZATIONS OF EKE¬
LAND S PRINCIPLE 379
7. EQUIVALENCIES 426
8. EKELAND S VARIATIONAL PRINCIPLE FOR VECTOR
VALUED FUNCTIONS 433
9. APPLICATIONS 444
• Existence of solutions for minimizing problems 444
• Coercivity condition 452
• A global variational principle on cones 454
• Density result 463
• Mountain pass lemma 464
• The Bishop Phelps theorem 477
• Clarke s fixed point theorem 480
• Borwein s e principle 484
• O accretive operators and surjectivity 488
• Zabreiko Krasnoselskii s theorem 494
• The drop property and the geometry of Banach spaces 497
• The drop property for arbitrary sets 519
10.REFERENCES 539
CHAPTER 5 555
Maximal Element Principles
1. INTRODUCTION 555
VII
CONTENTS
2. PRELIMINARIES 556
3. VARIATION ON ZORN S LEMMA 562
• Applications 567
• Comments 575
4. NEW MAXIMAL ELEMENT PRINCIPLES 576
• Applications 608
• A fixed point theorem for ordered sets 608
• Maximality and solvability 609
• Variable drops and general solvability 618
• A drop theorem 624
• Lipschitzianess tests 626
• Maximal element principles and general Newton
Kantorovich processes 633
• Comments 640
5. PARETO EFFICIENCY 641
6. REFERENCES 672
Symbol Index 685
Subject Index 691
VIII
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| any_adam_object | 1 |
| author | Hyers, Donald H. Isac, George Rassias, Themistocles M. 1951- |
| author_GND | (DE-588)120510057 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 514 - Topology |
| dewey-raw | 515.355 514.74 |
| dewey-search | 515.355 514.74 |
| dewey-sort | 3515.355 |
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| discipline | Mathematik |
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| id | DE-604.BV011749407 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:15:08Z |
| institution | BVB |
| isbn | 9810225342 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007927965 |
| oclc_num | 37462851 |
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| owner | DE-739 DE-20 DE-29T DE-706 |
| owner_facet | DE-739 DE-20 DE-29T DE-706 |
| physical | XIII, 699 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Hyers, Donald H. Verfasser aut Topics in nonlinear analysis & applications Donald H. Hyers ; George Isac ; Themistocles M. Rassias Singapore [u.a.] World Scientific 1997 XIII, 699 S. txt rdacontent n rdamedia nc rdacarrier Nonlinear functional analysis Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 s DE-604 Isac, George Verfasser aut Rassias, Themistocles M. 1951- Verfasser (DE-588)120510057 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007927965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hyers, Donald H. Isac, George Rassias, Themistocles M. 1951- Topics in nonlinear analysis & applications Nonlinear functional analysis Nichtlineare Analysis (DE-588)4177490-5 gnd |
| subject_GND | (DE-588)4177490-5 |
| title | Topics in nonlinear analysis & applications |
| title_auth | Topics in nonlinear analysis & applications |
| title_exact_search | Topics in nonlinear analysis & applications |
| title_full | Topics in nonlinear analysis & applications Donald H. Hyers ; George Isac ; Themistocles M. Rassias |
| title_fullStr | Topics in nonlinear analysis & applications Donald H. Hyers ; George Isac ; Themistocles M. Rassias |
| title_full_unstemmed | Topics in nonlinear analysis & applications Donald H. Hyers ; George Isac ; Themistocles M. Rassias |
| title_short | Topics in nonlinear analysis & applications |
| title_sort | topics in nonlinear analysis applications |
| topic | Nonlinear functional analysis Nichtlineare Analysis (DE-588)4177490-5 gnd |
| topic_facet | Nonlinear functional analysis Nichtlineare Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007927965&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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