Metric fixed point theory for multivalued mappings:
Gespeichert in:
| 1. Verfasser: | |
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| 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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