Metric fixed point theory for multivalued mappings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2000
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| Schriftenreihe: | Dissertationes mathematicae
389 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 39 S. |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Metric fixed point theory for multivalued mappings
Autor: Xu, Hong-Kun
Jahr: 2000
CONTENTS
0. Introduction....................................................................................................................................................5
1. Multivalued contractions............................................................................................................................6
1.1. Nadler s theorem..................................................................................................................................q
1.2. Reich s problem...........................................................................................................7
1.3. Weakly inward contractions..............................................................................................................11
1.4. Local contractions................................................................................................................................16
2. Multivalued nonexpansive mappings......................................................................................................18
2.1. Asymptotic centers..............................................................................................................................18
2.2. The Kirk-Massa theorem..................................................................................................................21
2.3. Inwardness and weak inwardness....................................................................................................22
2.4. Open problems......................................................................................................................................26
3. Random multivalued mappings................................................................................................................26
3.1. Introduction and preliminaries........................................................................................................27
3.2. Random contractions..........................................................................................................................30
3.3. Random nonexpansive mappings....................................................................................................32
Bibliography........................................................................................................................................................37
Abstract
Some new and recent results on the fixed point theory of multivalued contractions and nonexp-
ansive mappings are presented.
Discussions concerning Reich s problem are included. Existence of fixed points for weakly
inward contractions is proved. Local contractions are also discussed.
The Kirk-Massa theorem is extended to inward multivalued nonexpansive mappings. Using
an inequality characteristic of uniform convexity, another proof of Lim s theorem on weakly
inward multivalued nonexpansive mappings in a uniformly convex Banach space is included.
The fixed point set function of a random contraction is proved to be measurable. Lim s fixed
point theorem for nonexpansive self-mappings in a uniformly convex Banach space is randomized.
Also, the fixed point set function of a single-valued random nonexpansive mapping in a uniformly
smooth Banach space is shown to be measurable.
2000 Mathematics Subject Classification: Primary 47H04, 47H40, 47H10, 47H09; Secondary
46B20, 54C60, 65H25.
Key words and phrases: multivalued contraction, local contraction, multivalued nonexpansive
mapping, random contraction, random nonexpansive mapping, fixed point, random fixed
point, inward, weakly inward, metric space, uniformly convex Banach space.
Received 9.9.1999; revised version 4.6.2000.
|
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| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Xu, Hong-Kun Verfasser aut Metric fixed point theory for multivalued mappings Hong-Kun Xu Warszawa Polska Akad. Nauk, Inst. Matematyczny 2000 39 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 389 Fixed point theory Set-valued maps Fixpunktindex (DE-588)4154498-5 gnd rswk-swf Mehrdeutige Abbildung gnd rswk-swf Mehrdeutige Abbildung f Fixpunktindex (DE-588)4154498-5 s DE-604 Dissertationes mathematicae 389 (DE-604)BV000003039 389 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009256906&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xu, Hong-Kun Metric fixed point theory for multivalued mappings Dissertationes mathematicae Fixed point theory Set-valued maps Fixpunktindex (DE-588)4154498-5 gnd |
| subject_GND | (DE-588)4154498-5 |
| title | Metric fixed point theory for multivalued mappings |
| title_auth | Metric fixed point theory for multivalued mappings |
| title_exact_search | Metric fixed point theory for multivalued mappings |
| title_full | Metric fixed point theory for multivalued mappings Hong-Kun Xu |
| title_fullStr | Metric fixed point theory for multivalued mappings Hong-Kun Xu |
| title_full_unstemmed | Metric fixed point theory for multivalued mappings Hong-Kun Xu |
| title_short | Metric fixed point theory for multivalued mappings |
| title_sort | metric fixed point theory for multivalued mappings |
| topic | Fixed point theory Set-valued maps Fixpunktindex (DE-588)4154498-5 gnd |
| topic_facet | Fixed point theory Set-valued maps Fixpunktindex Mehrdeutige Abbildung |
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