Elements of probabilistic analysis: with applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Bucuresti
Ed. Acad. [u.a.]
1989
|
| Edition: | 2. ed. |
| Series: | Mathematics and its applications
East European series ; 36 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Einheitssacht.: Elemente de analiza probabilista cu aplicatii <rumän.> |
| Physical Description: | XI, 476 S. |
| ISBN: | 9027728380 |
Staff View
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Record in the Search Index
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| adam_text | Table of Contents
Series Editor s Preface IX
Introduction 1
CHAPTER 11 Probabilistic structures and related topics 3
1.1. Triangular Isorms, Triangular Functions and Proba¬
bilistic Structures 4
1.2. Probabilistic Measures of Noncompactness and
Applications 17
1.2.1. Kuratowski s Probabilistic Measures of 2sToncom
pactness 18
1.2.2. Hausdorff s Probabilistic Measures of Noncompact
ness 24
1.2.3. Some Remarks on the Probabilistic Measures of
Noncompactness on Probabilistic Linear Structures 25
CHAPTER 2i 3£easurable multivalued mappings and ran¬
domness 29
2.1. Preliminaries to the Probability Theory in Banach
Spaces . . 29
2.2. Measurable Multivalued Mappings and Random
Mappings 34
CHAPTER 31 Fixed point tJieory in probabilistic structures 45
3.1. Fixed Point Theorems for Mappings on Pit Spaces 46
3.1.1. Contraction Mappings on Complete PM Spaces . . 46
3.1.2. Relation between Fixed Point Theorems on Uni¬
form Spaces, Metric Spaces and PM Spaces ... 65
3.1.3. Some Classes of Generalized Contraction Mappings 90
3.1.4. Common Fixed Point Theorems for a Pair of Map¬
pings 123
3.1.5. Sequences of Probabilistic Contractions and Fixed
Points 132
3.1.6. Fixed Point Theorems for Mappings on [Nonarehi
medean P3f Spaees 142
3.1.7. Fixed Point Theorems for Multivalued Mappings
in PJf Spaces 158
VI TABLE OF CONTENTS
3.2. Fixed Point Theorems for Mappings on Random
formed Spaces 166
3.3. Some Results Regarding the Probabilistic Inner Pro¬
duct Spaces 188
3.4. Some Fixed Point Theorems for Mappings on Pro¬
babilistic Locally Convex Spaces 191
CHAPTER ¦i/Eandom fixed point theorems 207
4.1. Some Applications of Probabilistic Structures to
the Random Fixed Point Theory 208
4.2. Some Random Fixed Point Theorems for Conti¬
nuous Random Operators 227
4.3. Random Fixed Point Theorems for Multivalued
Random Operators 244
4.4. Fixed Point Theorems for Random Singlevalued
and Multivalued Operators on Stochastic Domains 261
4.4.1. Random Fixed Point Theorems for Random Ope¬
rators with Stochastic Domains 261
4.4.2. Random Fixed Point Theorems for Multivalued
Random Operators with Stochastic Domains . . 277
CHAPTER 5j Applications of the fixed point theory to ran¬
dom operator equations 287
5.1. Some Applications of the Fixed Point Theorems to
Probabilistic Structures 287
5.2. Some Extremum Problems for Functionals on
PM Spaces and Stochastic Optimization 293
5.3. Applications of Random Fixed Point Theorems to
Random Differential and Integral Equations . . . 301
5.4. Applications of Random Fixed Point Theorems to
Stochastic Approximation 326
CHAPTER 61 Some analysis problems and methods for
random equations 335
6.1. Some Examples on the Use of the Selection Theorem
Approach 337
6.2 Approximate Solution of Random Equations . . . 340
6.2.1. Iterative Methods , 340
6.2.2. Projection Methods 347
6.2.3. Approximate Solution of Random Nonlinear
Equations by Random Contractors 358
6.2.4. On a General Convergence Theory for Solutions
of Approximations . 364
6.3. jSTonlinear Random Equations Involving Certain
Types of Operators . 370
TABLE OF CONTENTS VII
CHAPTER TjSome applications of random operators . . 389
7.1. Bandom Equations and Wave Propagation in Ban
dom Media 389
7.1.1. On Two Classes of Methods 390
7.1.2. Perturbation theory Approach 391
7.1.3. Applications to Wave Propagation in Continuous
Media 393
7.2. A Bandom Integral Equation in Turbulence Theory 397
7.3. Bandom Vibration of Elastic Strings and Bars . . 400
7.4. Bandom Methods in Stream Temperature Modelling 406
7.5. Stochastic Models for Stream Pollution 409
7.6. A Stochastic Model for Chemotherapy 414
7.7. An Application of Bandom Contractors in Popu¬
lation Growth Problems 419
7.8. A Bandom Equation in Telephone Traffic Theory 425
7.9. Stochastic Operators and Stochastic Systems . . 427
7.10. Stochastic Nonlinear Programming and Stochastic
Optimal Control Problems 436
Beferences 447
Author Index . , , 471
Subject Index 473
|
| adam_txt |
Table of Contents
Series Editor's Preface IX
Introduction 1
CHAPTER 11 Probabilistic structures and related topics 3
1.1. Triangular Isorms, Triangular Functions and Proba¬
bilistic Structures 4
1.2. Probabilistic Measures of Noncompactness and
Applications 17
1.2.1. Kuratowski's Probabilistic Measures of 2sToncom
pactness 18
1.2.2. Hausdorff's Probabilistic Measures of Noncompact
ness 24
1.2.3. Some Remarks on the Probabilistic Measures of
Noncompactness on Probabilistic Linear Structures 25
CHAPTER 2i'3£easurable multivalued mappings and ran¬
domness 29
2.1. Preliminaries to the Probability Theory in Banach
Spaces \ . . \ 29
2.2. Measurable Multivalued Mappings and Random
Mappings 34
CHAPTER 31 Fixed point tJieory in probabilistic structures 45
3.1. Fixed Point Theorems for Mappings on Pit Spaces 46
3.1.1. Contraction Mappings on Complete PM Spaces . . 46
3.1.2. Relation between Fixed Point Theorems on Uni¬
form Spaces, Metric Spaces and PM Spaces . 65
3.1.3. Some Classes of Generalized Contraction Mappings 90
3.1.4. Common Fixed Point Theorems for a Pair of Map¬
pings 123
3.1.5. Sequences of Probabilistic Contractions and Fixed
Points 132
3.1.6. Fixed Point Theorems for Mappings on [Nonarehi
medean P3f Spaees 142
3.1.7. Fixed Point Theorems for Multivalued Mappings
in PJf Spaces 158
VI TABLE OF CONTENTS
3.2. Fixed Point Theorems for Mappings on Random
formed Spaces 166
3.3. Some Results Regarding the Probabilistic Inner Pro¬
duct Spaces 188
3.4. Some Fixed Point Theorems for Mappings on Pro¬
babilistic Locally Convex Spaces 191
CHAPTER ¦i/Eandom fixed point theorems 207
4.1. Some Applications of Probabilistic Structures to
the Random Fixed Point Theory 208
4.2. Some Random Fixed Point Theorems for Conti¬
nuous Random Operators 227
4.3. Random Fixed Point Theorems for Multivalued
Random Operators 244
4.4. Fixed Point Theorems for Random Singlevalued
and Multivalued Operators on Stochastic Domains 261
4.4.1. Random Fixed Point Theorems for Random Ope¬
rators with Stochastic Domains 261
4.4.2. Random Fixed Point Theorems for Multivalued
Random Operators with Stochastic Domains . . 277
CHAPTER 5j'Applications of the fixed point theory to ran¬
dom operator equations 287
5.1. Some Applications of the Fixed Point Theorems to
Probabilistic Structures 287
5.2. Some Extremum Problems for Functionals on
PM Spaces and Stochastic Optimization 293
5.3. Applications of Random Fixed Point Theorems to
Random Differential and Integral Equations . . . 301
5.4. Applications of Random Fixed Point Theorems to
Stochastic Approximation 326
CHAPTER 61 Some analysis problems and methods for
random equations 335
6.1. Some Examples on the Use of the Selection Theorem
Approach 337
6.2 Approximate Solution of Random Equations . . . 340
6.2.1. Iterative Methods , 340
6.2.2. Projection Methods 347
6.2.3. Approximate Solution of Random Nonlinear
Equations by Random Contractors 358
6.2.4. On a General Convergence Theory for Solutions
of Approximations . 364
6.3. jSTonlinear Random Equations Involving Certain
Types of Operators . 370
TABLE OF CONTENTS VII
CHAPTER TjSome applications of random operators . . 389
7.1. Bandom Equations and Wave Propagation in Ban
dom Media 389
7.1.1. On Two Classes of Methods 390
7.1.2. Perturbation theory Approach 391
7.1.3. Applications to Wave Propagation in Continuous
Media 393
7.2. A Bandom Integral Equation in Turbulence Theory 397
7.3. Bandom Vibration of Elastic Strings and Bars . . 400
7.4. Bandom Methods in Stream Temperature Modelling 406
7.5. Stochastic Models for Stream Pollution 409
7.6. A Stochastic Model for Chemotherapy 414
7.7. An Application of Bandom Contractors in Popu¬
lation Growth Problems 419
7.8. A Bandom Equation in Telephone Traffic Theory 425
7.9. Stochastic Operators and Stochastic Systems . . 427
7.10. Stochastic Nonlinear Programming and Stochastic
Optimal Control Problems 436
Beferences 447
Author Index . , , 471
Subject Index 473 |
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| author | Constantin, Gheorge Istrăţescu, Ioana |
| author_facet | Constantin, Gheorge Istrăţescu, Ioana |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 9027728380 |
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| physical | XI, 476 S. |
| publishDate | 1989 |
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| publisher | Ed. Acad. [u.a.] |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications : East European series |
| spelling | Constantin, Gheorge Verfasser aut Elements of probabilistic analysis with applications 2. ed. Bucuresti Ed. Acad. [u.a.] 1989 XI, 476 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications : East European series 36 Einheitssacht.: Elemente de analiza probabilista cu aplicatii <rumän.> Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Fixpunkttheorie (DE-588)4293945-8 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s 1\p DE-604 Istrăţescu, Ioana Verfasser aut Mathematics and its applications East European series ; 36 (DE-604)BV000006709 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015400051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Constantin, Gheorge Istrăţescu, Ioana Elements of probabilistic analysis with applications Mathematics and its applications Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Fixpunkttheorie (DE-588)4293945-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4293945-8 (DE-588)4079013-7 |
| title | Elements of probabilistic analysis with applications |
| title_auth | Elements of probabilistic analysis with applications |
| title_exact_search | Elements of probabilistic analysis with applications |
| title_exact_search_txtP | Elements of probabilistic analysis with applications |
| title_full | Elements of probabilistic analysis with applications |
| title_fullStr | Elements of probabilistic analysis with applications |
| title_full_unstemmed | Elements of probabilistic analysis with applications |
| title_short | Elements of probabilistic analysis |
| title_sort | elements of probabilistic analysis with applications |
| title_sub | with applications |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Fixpunkttheorie (DE-588)4293945-8 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung Fixpunkttheorie Wahrscheinlichkeitstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015400051&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
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