Fixed point theory:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cluj-Napoca
Cluj Univ. Press
2008
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 509 S. |
| ISBN: | 9789736108105 |
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MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV036571466 | ||
| 003 | DE-604 | ||
| 005 | 20100913 | ||
| 007 | t | ||
| 008 | 100719s2008 |||| 00||| eng d | ||
| 020 | |a 9789736108105 |9 978-973-610-810-5 | ||
| 035 | |a (OCoLC)705674162 | ||
| 035 | |a (DE-599)BVBBV036571466 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 | ||
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 100 | 1 | |a Rus, Ioan A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fixed point theory |c Ioan A. Rus ; Adrian Petruşel ; Gabriela Petruşel |
| 264 | 1 | |a Cluj-Napoca |b Cluj Univ. Press |c 2008 | |
| 300 | |a XX, 509 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Fixpunkttheorie |0 (DE-588)4293945-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fixpunkttheorie |0 (DE-588)4293945-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Petruşel, Adrian |e Verfasser |4 aut | |
| 700 | 1 | |a Petruşel, Gabriela |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020492582 | ||
Record in the Search Index
| _version_ | 1804143153586896896 |
|---|---|
| adam_text | Contents
Introduction
їх
1
Set-theoretic aspects of the fixed point theory
1
1.0
Basic notions and results
...................... 1
1.1
Total /-variant subsets and fixed points
............. 5
1.2
Invariant subsets
.......................... 6
1.3 Ä-contractions ........................... 7
1.4
Schroder s pairs
........................... 9
2
Order-theoretic aspects of the fixed point theory
11
2.0
Basic notions and results
......................
ц
2.1
Other fixed point theorems in ordered sets
............ 17
2.2
Fixed point theorems for Boolean type operators
........ 18
2.3
Fixed point theorems for
non
self-operators
........... 18
3
Generalized contractions on metric spaces
21
3.0
Preliminaries
............................ 21
3.0.1
Topological spaces
..................... 21
3.0.2
Metric spaces
........................ 22
3.0.3
Comparison functions
................... 25
3.1
Operators on metric spaces
.................... 26
3.1.1
Basic concepts
....................... 26
3.1.2
Generalized contractions
.................. 27
3.2
Basic fixed point principles
.................... 30
3.3
Fixed point theorems on sets with two metrics
......... 39
ii
__________________________________________________CONTENTS
3.4
Basic
problems of the metric fixed point theory
......... 41
3.5
Equivalent statements
....................... 44
3.6
Generalized contractions and quasibounded operators
..... 48
4
Generalized contractions on g.m.s. (d(x,y)
є
M.+)
51
4.0
Generalized metric spaces (d(x,
у) Є Ж+)
............. 51
4.1
Fixed point theory in b-metric spaces
.............. 52
4.2
Fixed point theorems in partial metric spaces
.......... 54
4.2.1
Partial metric spaces
.................... 54
4.2.2
Fixed point theory in partial metric spaces
....... 55
4.3
Fixed point theory in gauge spaces
................ 60
4.3.1
Uniform spaces. Gauge spaces
............... 60
4.3.2
Complete gauge structures
................ 62
4.3.3
Fixed point theory in gauge spaces
............ 63
4.3.4
Other results
........................ 67
4.4
Fixed point theorems in semimetric spaces
............ 68
5
Generalized contractions on g.m.s. (d(x,
у) є
R+
U
{+00}) 69
5.0
Generalized metric space (d(x,
у) Є
JR+
U
+00) ......... 69
5.1
Fixed point theory in g.m.s. (d(x,
у) Є Ж+
U
{+00}) ...... 71
6
Generalized contractions on G-metric spaces
77
6.0
Basic concepts
........................... 77
6.0.1
L-spaces
........................... 77
6.0.2
Ordered Banach spaces
.................. 80
6.0.3
Convergent to zero matrices
................ 81
6.0.4
Infinite matrices
...................... 81
6.1
Fixed point theorems in Rm-metric spaces
............ 82
6.2
Fixed point theorems in a s(3R)-metric spaces
.......... 86
6.3
Other results
............................ 88
7
Generalized contractions on probabilistic metric spaces
95
7.0
Probabilistic metric spaces
..................... 95
7.1
Contractions on probabilistic metric spaces
........... 98
CONTENTS
111
7.2
Fixed point principles for multivalued operators
.........100
8 Nonexpansive
operators
105
8.0
Preliminaries
............................ 105
8.0.1
The geometry of the Banach spaces
........... 105
8.0.2
Averaged operators
..................... 107
8.1
Fixed point theory of
nonexpansive
operators
.......... 107
8.2
Jaggi-nonexpansive operators
................... 110
8.3 Nonexpansive
operators on nonconvex sets
............ 110
8.4 Nonexpansive
operators on convex metric spaces
........
Ill
8.5
Other results
............................ 112
9
Expansive, noncontractive and dilating operators
113
9.0
Basic notions and results
...................... 113
9.1
Dilating operators
......................... 115
9.2
Noncontractive operators
..................... 116
9.3
Fixed points, zeros and surjectivity
................ 116
10
Picard
and weakly
Picard
operators
119
10.0
Basic notions
............................ 119
10.1
The structure theorem of WPOs
................. 120
10.2
Data dependence of the fixed point set
.............. 122
10.3
Picard
operators on ordered metric spaces
............ 123
10.4
WPOs on ordered metric spaces
.................. 124
10.5
Fiber WPOs
............................ 125
11
Multivalued generalized contractions on metric spaces
127
11.0
Preliminaries
............................ 127
11.0.1
Functionate on P(X)
.................... 127
11.0.2
Multivalued operators on topological spaces
....... 130
11.0.3
Multivalued generalized contractions
........... 131
11.1
Basic fixed point principles for multivalued operators
...... 132
11.2
Basic strict fixed point principles for multivalued operators
. . 136
11.3
Properties of the fixed point set
.................. 141
iv__________________________________________________CONTENTS
11.4
Fixed point theorems on a set with two metrics
......... 144
11.5
Fixed point theorems for multivalued
nonexpansive
operators
. 146
11.6
Multivalued weakly
Picard
operators
............... 148
11.7
Well-posedness of the fixed point problems
............ 150
11.8
Other results
............................ 153
11.9
Applications
............................153
12
Multivalued generalized contractions on g.m.s.
155
12.0
d(x,y)
ЄМ
+UÍ+oo}
........................
155
12.1
d{x,y)
ЕЩ
.............................160
12.2
ò-metric
spaces
...........................161
12.3
Gauge spaces
............................164
13
Compactness, convexity and fixed points
169
13.0
Introduction
.............................170
13.1
Abstract measures of non-compactness and fixed points
.... 170
13.2
Abstract measures of nonconvexity and fixed points
......172
13.3
Convexity and decomposability
..................173
14
Common fixed points
177
14.0
Set-theoretical aspects of the common fixed point theory
.... 177
14.1
Order-theoretical aspects of the common fixed point theory
. . 178
14.2
Generalized contraction pairs
................... 179
14.3
Basic problems of the metrical common fixed point theory
. . . 180
14.4
Almost common fixed points of totally
nonexpansive
families of
operators
.............................. 182
14.5
Multivalued operators
....................... 184
15
Coincidence point theory
187
15.0
C(f,g) and Fg-iof
.........................187
15.1
C(f,g) and F^-i
.........................189
15.2
Data dependence
..........................190
15.3
Nearness and coincidence
.....................191
15.4
Coincidence point theory via
Picard
operators
..........192
CONTENTS
15.5
Coïncidence
point theory on convex cones
............193
15.6
Coincidence point theory for multivalued operators
.......194
15.7
Other results
............................201
16
Topological degree theory
203
16.0
Preliminaries
............................204
16.1
Brouwer s degree
..........................205
16.2
Leray-Schauder s degree
......................206
16.3
Topological degree theory for multivalued operators
......208
16.4
Coincidence degree theory
.....................209
17
Topological spaces with the fixed point property
213
17.0
Topological spaces with the fixed point property
........ 214
17.1
Equivalent statements with the f.p.p
................ 215
17.2
Brouwer
fixed point theorem
................... 216
17.3
Generalizations of the
Brouwer
fixed point theorem
....... 218
17.4
Multivalued operators
....................... 219
17.5
Continuity, convexity, compactness and fixed points
...... 222
17.6
Other results
............................ 222
18
Fixed point structures
225
18.0
Preliminaries
............................ 225
18.1
Fixed point structures. Examples
................. 227
18.2
Functionals with the intersection property. Examples
...... 228
18.3
Compatible pair with a fixed point structure
.......... 228
18.4
(Θ,
(¿^-contraction and (^-condensing operators
.......... 229
18.5
First general fixed point principle
................. 230
18.6
Second general fixed point principle
............... 232
18.7
Fixed point structures with the common fixed point property
. 233
18.8
Fixed point structures with the coincidence property
...... 235
18.9
Other results
............................ 235
19
Fixed point structures for multivalued operators
237
19.0
Notations
..............................237
vi
__________________________________________________CONTENTS
19.1
Examples of fixed point structures for multivalued operators
. . 237
19.2
Examples of strict fixed point structures
............. 239
19.3
(Θ,
(¿^-contractions and ^-condensing operators
......... 240
19.4
First general fixed point principle for multivalued operators
. . 241
19.5
Second general fixed point principle for multivalued operators
. 244
19.6
Other results
............................ 244
20
Fixed point theory for operators on product spaces
247
20.0
Basic problems
...........................247
20.1
f :XxY
-*X xY
........................248
20.2 ƒ :
Xk
-+
X
.............................249
20.3
Other results
............................250
21
Fixed point theory for nonself operators
251
21.0
Basic fixed point principles for nonself operators
........ 252
21.1
Continuation principles for generalized contractions
....... 254
21.2
A general continuation principle
................. 255
21.3
Retractible operators
........................ 256
21.4
Basic fixed point principles for multivalued nonself operators
. 258
21.5
Continuation principles for multivalued operators
........ 262
21.6
Retractible multivalued operators
................. 264
21.7
The case of the strict fixed point structures
........... 265
22
A generic view on the fixed point theory
267
22.0
Preliminaries
............................267
22.1
Generic aspects on Schauder s theorem
..............268
22.2
Generic aspects on Fan-Glicksberg s theorem
..........269
22.3
Other results
............................270
23
Iterated function (operator) systems
271
23.0
Set-to-set operators
......................... 271
23.1
Iterated
Picard
operator systems
................. 273
23.2
Iterated multivalued operator systems
.............. 275
24
Other results
279
CONTENTS____________________________________________________
vii
24.1
Ultra-methods in metric fixed point theory
........... 279
24.2
Fixed point theorems in Kasahara spaces
............ 280
24.3
Iterative test of Edelstein
..................... 281
24.4
Fixed point theorems in 2-metric spaces
............. 282
24.5
Y-contractions
........................... 282
24.6
Fixed point theorems for Darboux functions
........... 284
24.7
Iterated functions on
R
...................... 285
24.8
Iterated functions on
С
...................... 286
24.9
Fixed point theory in Cn and in a complex Banach space
. . . 287
24.10
Fixed point theory in ordered linear spaces
........... 288
24.11
Minimal displacement of points under operators
........ 288
24.12
Almost and approximate fixed point property
......... 289
24.13
Periodic points
........................... 290
24.14
Invariability of the fixed point set of a multivalued operator
. 292
24.15
Stability of the fixed point property
............... 292
24.16
Relative fixed point property
................... 293
24.17
Antipodal points
.......................... 293
24.18
Classification of fixed points
................... 294
24.19
Fixed point theory for fuzzy operators
.............. 294
24.20
Fixed point theory in algebraic structures
............ 295
24.21
Fixed point theory in algebraic topology
............ 295
24.22
Finite commutative family of operators
............. 296
24.23
Common fixed points for commuting families of operators
. . . 296
24.24
Asymptotic fixed point theory
.................. 297
24.25
Fixed point theory in categories
................. 299
24.26
Maximal fixed point structures
.................. 300
24.27
The computation of fixed points
................. 302
24.28
Bifurcation theory
......................... 303
24.29
Surjectivity, injectivity,
invariance
of domain and fixed points
. 304
24.30
Implicit operators and fixed points
................ 305
24.31
Caristi selections for multivalued operators
........... 306
24.32
Applications of the fixed point theory
.............. 307
24.32.1
Applications to functional equations
........... 307
viii
_____________________________________________________CONTENTS
24.32.2
Applications
to differential equations
.......... 308
24.32.3
Applications to integral equations
............ 308
24.32.4
Applications to functional-differential equations
.... 309
24.32.5
Applications to functional-integral equations
...... 309
24.32.6
Applications to differential and integral inclusions
. . . 309
24.32.7
Applications to set differential equations
........ 310
24.32.8
Applications to mathematical economics
........ 310
24.32.9
Applications to Informatics
................ 310
24.32.10
Other applications
.................... 311
1
Romanian Bibliography of the Fixed Point Theory
315
2
General References
377
List of Symbols
477
Index of Terms
481
Authors Index
488
|
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| author | Rus, Ioan A. Petruşel, Adrian Petruşel, Gabriela |
| author_facet | Rus, Ioan A. Petruşel, Adrian Petruşel, Gabriela |
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| building | Verbundindex |
| bvnumber | BV036571466 |
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| ctrlnum | (OCoLC)705674162 (DE-599)BVBBV036571466 |
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| id | DE-604.BV036571466 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:43:08Z |
| institution | BVB |
| isbn | 9789736108105 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020492582 |
| oclc_num | 705674162 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XX, 509 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cluj Univ. Press |
| record_format | marc |
| spelling | Rus, Ioan A. Verfasser aut Fixed point theory Ioan A. Rus ; Adrian Petruşel ; Gabriela Petruşel Cluj-Napoca Cluj Univ. Press 2008 XX, 509 S. txt rdacontent n rdamedia nc rdacarrier Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Fixpunkttheorie (DE-588)4293945-8 s DE-604 Petruşel, Adrian Verfasser aut Petruşel, Gabriela Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rus, Ioan A. Petruşel, Adrian Petruşel, Gabriela Fixed point theory Fixpunkttheorie (DE-588)4293945-8 gnd |
| subject_GND | (DE-588)4293945-8 |
| title | Fixed point theory |
| title_auth | Fixed point theory |
| title_exact_search | Fixed point theory |
| title_full | Fixed point theory Ioan A. Rus ; Adrian Petruşel ; Gabriela Petruşel |
| title_fullStr | Fixed point theory Ioan A. Rus ; Adrian Petruşel ; Gabriela Petruşel |
| title_full_unstemmed | Fixed point theory Ioan A. Rus ; Adrian Petruşel ; Gabriela Petruşel |
| title_short | Fixed point theory |
| title_sort | fixed point theory |
| topic | Fixpunkttheorie (DE-588)4293945-8 gnd |
| topic_facet | Fixpunkttheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rusioana fixedpointtheory AT petruseladrian fixedpointtheory AT petruselgabriela fixedpointtheory |