Convex and set-valued analysis: selected topics
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2017]
|
| Series: | De Gruyter graduate
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | VIII, 201 Seiten 24 cm |
| ISBN: | 9783110460285 3110460289 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804177410222981120 |
|---|---|
| adam_text | Contents
Preface-V
Part I: Convex analysis
1 Convex sets and their properties----3
2 The convex hull of a set. The interior of convex sets-7
3 The affine hull of sets. The relative interior of convex sets-13
4 Separation theorems for convex sets----21
5 Convex functions----29
6 Closedness, boundedness, continuity, and Lipschitz property
of convex functions---37
7 Conjugate functions---45
8 Support functions---51
9 Differentiability of convex functions and the subdifferential-59
10 Convex cones----69
11 A little more about convex cones in infinite-dimensional spaces-
12 A problem of linear programming----79
13 More about convex sets and convex hulls---83
Part II: Set-valued analysis
14
15
introduction to the theory of topological and metric spaces
The Hausdorff metric and the distance between sets------95
91
VIII
Contents
16 Some fíne properties of the Hausdorff metric--103
16.1 Hausdorff distance between sets satisfying the Bolzano-Weierstrass
condition----103
16.2 Hausdorff distance between subsets of normed spaces----105
17 Set-valued maps. Upper semicontinuous and lower semicontinuous
set-valued maps-----109
18 A base of topology of the space (X)-----121
19 Measurable set-valued maps. Measurable selections and measurable
choice theorems-----123
20 The superposition set-valued operator---129
21 The Michael theorem and continuous selections. Lipschitz selections.
Single-valued approximations-----135
22 Special selections of set-valued maps---141
23 Differential inclusions--149
24 Fixed points and coincidences of maps in metric spaces--155
24.1 The case of single-valued maps---155
24.2 The case of set-valued maps---160
25 Stability of coincidence points and properties of covering maps-165
26 Topological degree and fixed points of set-valued maps
in Banach spaces----171
26.1 Topological degree of single-valued maps--171
26.2 Topological degree of set-valued maps---180
27 Existence results for differential inclusions
via the fixed point method---187
Notation----191
Bibliography----195
Index
199
|
| any_adam_object | 1 |
| author | Arutjunov, Aram Vladimirovic 1956- Obuchovskij, Valerij 1947- |
| author_GND | (DE-588)1056101636 (DE-588)122814215 |
| author_facet | Arutjunov, Aram Vladimirovic 1956- Obuchovskij, Valerij 1947- |
| author_role | aut aut |
| author_sort | Arutjunov, Aram Vladimirovic 1956- |
| author_variant | a v a av ava v o vo |
| building | Verbundindex |
| bvnumber | BV044245690 |
| classification_rvk | SK 620 SK 400 |
| ctrlnum | (OCoLC)941673035 (DE-599)BVBBV044245690 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044245690 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:47:38Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110460285 3110460289 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029650900 |
| oclc_num | 941673035 |
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| owner | DE-19 DE-BY-UBM DE-739 DE-703 |
| owner_facet | DE-19 DE-BY-UBM DE-739 DE-703 |
| physical | VIII, 201 Seiten 24 cm |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spelling | Arutjunov, Aram Vladimirovic 1956- Verfasser (DE-588)1056101636 aut Convex and set-valued analysis selected topics Aram V. Arutyunov, Valeri Obukhovskii Berlin ; Boston De Gruyter [2017] VIII, 201 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Mengenwertige Funktion (DE-588)4342651-7 gnd rswk-swf Mengenwertige Abbildung (DE-588)4270772-9 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Fachhochschul-/Hochschulausbildung Konvexe Analysis (DE-588)4138566-4 s Mengenwertige Abbildung (DE-588)4270772-9 s Mengenwertige Funktion (DE-588)4342651-7 s DE-604 Obuchovskij, Valerij 1947- Verfasser (DE-588)122814215 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-046030-8 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-046041-4 B:DE-101 application/pdf http://d-nb.info/1082766437/04 Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029650900&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arutjunov, Aram Vladimirovic 1956- Obuchovskij, Valerij 1947- Convex and set-valued analysis selected topics Mengenwertige Funktion (DE-588)4342651-7 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Konvexe Analysis (DE-588)4138566-4 gnd |
| subject_GND | (DE-588)4342651-7 (DE-588)4270772-9 (DE-588)4138566-4 |
| title | Convex and set-valued analysis selected topics |
| title_auth | Convex and set-valued analysis selected topics |
| title_exact_search | Convex and set-valued analysis selected topics |
| title_full | Convex and set-valued analysis selected topics Aram V. Arutyunov, Valeri Obukhovskii |
| title_fullStr | Convex and set-valued analysis selected topics Aram V. Arutyunov, Valeri Obukhovskii |
| title_full_unstemmed | Convex and set-valued analysis selected topics Aram V. Arutyunov, Valeri Obukhovskii |
| title_short | Convex and set-valued analysis |
| title_sort | convex and set valued analysis selected topics |
| title_sub | selected topics |
| topic | Mengenwertige Funktion (DE-588)4342651-7 gnd Mengenwertige Abbildung (DE-588)4270772-9 gnd Konvexe Analysis (DE-588)4138566-4 gnd |
| topic_facet | Mengenwertige Funktion Mengenwertige Abbildung Konvexe Analysis |
| url | http://d-nb.info/1082766437/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029650900&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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