Classification of Lipschitz mappings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, FL [u.a.]
CRC Press
2014
|
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 224 S. graph. Darst. |
| ISBN: | 9781466595217 1466595213 |
Staff View
MARC
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| 245 | 1 | 0 | |a Classification of Lipschitz mappings |c Lukasz Piasecki |
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| 300 | |a X, 224 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150649780174848 |
|---|---|
| adam_text | Contents
Introduction
1
1
The Lipschitz condition
5
1.1
Nonlinear spectral radius
.................... 5
1.2
Uniformly lipschitzian mappings
................ 8
2
Basic facts on Banach spaces
11
2.1
Convexity
............................. 12
2.2
The operator norm
....................... 17
2.3
Dual spaces,
reflexivity,
the weak, and weak* topologies
... 17
3
Mean Lipschitz condition
25
3.1 Xonexpansive
and mean
nonexpansive
mappings in Banach
spaces
............................... 25
3.2
General case
........................... 38
4
On the Lipschitz constants for iterates of mean lipschitzian
mappings
41
4.1
A bound for Lipschitz constants of iterates
.......... 41
4.2
A bound for the constant
кж(Т)
................ 62
4.3
Moving averages in Banach spaces
............... 69
4.4
A bound for the constant ko(T)
................ 72
4.5
More about k{Tn). ko(T), and
кж(Т)
............. 77
5
Subclasses determined by /»-averages
85
5.1
Basic definitions and observations
............... 85
5.2
A bound for
к(Тп),
kx(T), and
ко(Т)
............. 89
5.3
On the moving p-averages
.................... 94
6
Mean contractions
6.1
Classical Banachs contractions
................. 95
6.2
On characterizations of contractions
.............. 98
6.3
On the rate of convergence of iterates
............. 100
IX
χ
Contents
7 Nonexpansive
mappings in Banach space
103
7.1
The asymptotic center technique
................ 103
7.2
Minimal invariant sets and normal structure
.........
Ill
7.3
Uniformly
nonsquare,
uniformly noncreasy. and reflexive
Banach spaces
.......................... 123
7.4
Remarks on the stability of f.p.p
................ 124
7.5
The case of lx
.......................... 130
8
Mean
nonexpansive
mappings
139
8.1
Some new results of stability type
............... 139
8.2
Sequential approximation of fixed points
........... 150
8.3
The case of
η
= 3 ........................ 153
8.4
On the structure of the fixed points set
............ 159
9
Mean lipschitzian mappings with
к
> 1 163
9.1
Losing compactness in Brouwer s Fixed Point Theorem
. . . 163
9.2
Retracting onto balls in Banach spaces
............ 169
9.3
Minimal displacement
...................... 180
9.4
Optimal retractions
....................... 197
9.5
Generalized characteristics of minimal displacement
..... 205
Bibliography
217
Index
223
Mathematics
Classification of Lipschitz Mappings
Deep understanding of the properties of Lipschitzian mappings is important
for all levels of study in many branches of mathematics. This book by
Łukasz
Piasecki is a good choice for achieving such an understanding in the framework
of mappings in general metric spaces, in particular, Banach spaces. Moreover,
it gives new insight into the theory of Lipschitzian mappings via a study of the
mean Lipschitz condition.
...
The book is written in a very clear and reader-friendly
way. The author gives many examples illustrating various aspects of presented
results.
— Stanislaw
Prus,
Marie Curie-Sklodowska University
...
a self-contained, readable, and precise course on the subject.
...
Besides the
presentation of the theory, the true value of the book lies in a collection of cleverly
chosen interesting examples.
— Kazimierz Goebel.
Maria Curie-Sklodowska University
I strongly recommend this book for advanced undergraduate and graduate
students
...
The reader
wili
find a new classification of this kind of mapping as
well as many examples and illustrations designed to help the reader understand
the definitions, properties, and results.
...
I also recommend this book for analysts
or mathematicians who are looking for new topics to research.
— Victor Perez-Garcia, University of Veracruz
Classification of Lipschitz Mappings presents a systematic, self-contained
treatment of a new. more precise classification of Lipschitz mappings and
its application in many topics of metric fixed point theory. The mean Lipschitz
condition introduced by Goebel,
Japón
Pineda, and Sims is relatively easy to
check and turns out to satisfy several principles: regulating the possible growth of
the sequence of Lipschitz constants k<T>, ensuring good estimates for k.tTt and
kiT/, and providing some new results in metric fixed point theory.
CRC Press
Tavior
&
Francis Crouo
informa
6Ö00
Broken Sound Parkwd
.
Suite
300.
80c T487
Ыта
Avenue
New York, NY
Î0017
2
ark Square, Miiton Park
Afcwłodon,
Oxort OX14 4RN. UK
ΚΞ071Μ
ISBN:
470-1-4^5-4521-7
900Ű0
|
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| bvnumber | BV041215518 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)870209128 (DE-599)BVBBV041215518 |
| discipline | Mathematik |
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| id | DE-604.BV041215518 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:42:17Z |
| institution | BVB |
| isbn | 9781466595217 1466595213 |
| language | English |
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| physical | X, 224 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Piasecki, Lukasz Verfasser aut Classification of Lipschitz mappings Lukasz Piasecki Boca Raton, FL [u.a.] CRC Press 2014 X, 224 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Abbildung Mathematik (DE-588)4000044-8 gnd rswk-swf Lipschitz-Bedingung (DE-588)4167811-4 gnd rswk-swf Abbildung Mathematik (DE-588)4000044-8 s Lipschitz-Bedingung (DE-588)4167811-4 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190162&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190162&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Piasecki, Lukasz Classification of Lipschitz mappings Abbildung Mathematik (DE-588)4000044-8 gnd Lipschitz-Bedingung (DE-588)4167811-4 gnd |
| subject_GND | (DE-588)4000044-8 (DE-588)4167811-4 |
| title | Classification of Lipschitz mappings |
| title_auth | Classification of Lipschitz mappings |
| title_exact_search | Classification of Lipschitz mappings |
| title_full | Classification of Lipschitz mappings Lukasz Piasecki |
| title_fullStr | Classification of Lipschitz mappings Lukasz Piasecki |
| title_full_unstemmed | Classification of Lipschitz mappings Lukasz Piasecki |
| title_short | Classification of Lipschitz mappings |
| title_sort | classification of lipschitz mappings |
| topic | Abbildung Mathematik (DE-588)4000044-8 gnd Lipschitz-Bedingung (DE-588)4167811-4 gnd |
| topic_facet | Abbildung Mathematik Lipschitz-Bedingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190162&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190162&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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