Convex functions and related functional equations: selected topics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cluj-Napoca
Presa Universitară Clujeană
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 390 S. |
| ISBN: | 9789736107177 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV036754322 | ||
| 003 | DE-604 | ||
| 005 | 20101216 | ||
| 007 | t | ||
| 008 | 101103s2008 |||| 00||| eng d | ||
| 020 | |a 9789736107177 |9 978-973-610-717-7 | ||
| 035 | |a (OCoLC)705943299 | ||
| 035 | |a (DE-599)BVBBV036754322 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 | ||
| 084 | |a SK 420 |0 (DE-625)143238: |2 rvk | ||
| 100 | 1 | |a Breckner, Wolfgang W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Convex functions and related functional equations |b selected topics |c Wolfgang W. Breckner ; Tiberiu Trif |
| 264 | 1 | |a Cluj-Napoca |b Presa Universitară Clujeană |c 2008 | |
| 300 | |a XIV, 390 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Konvexe Funktion |0 (DE-588)4139679-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionalgleichung |0 (DE-588)4018923-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvexe Funktion |0 (DE-588)4139679-0 |D s |
| 689 | 0 | 1 | |a Funktionalgleichung |0 (DE-588)4018923-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Trif, Tiberiu |e Sonstige |4 oth | |
| 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=020671522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020671522 | ||
Datensatz im Suchindex
| _version_ | 1804143418587217920 |
|---|---|
| adam_text | Contents
Preface
ix
List of Symbols
xi
Part I: Preliminaries
Elements of Topology
3
1.1
Preordered Sets
........................... 3
1.2
The Set of Extended Real Numbers
................ 5
1.3
Topological Spaces
......................... 7
1.4
Sets in a Topological Space
.................... 14
1.5
Semicontinuous Functions
..................... 24
1.6
Topological Linear Spaces
..................... 31
Elements of Linear Space Theory
37
2.1
Convex Sets
............................. 37
2.2
Finite-Dimensional Sets
...................... 50
2.3
The Algebraic Interior and the Relative Algebraic Interior
... 61
2.4
Convex Functions
.......................... 72
2.5
Sublinear
Functions
........................ 82
Part II: Basic Properties of Convex Functions
Convex Functions on the Real Line
91
3.1
Reduction of a Convex Function to a Convex Function of a Real
Variable
............................... 91
3.2
Characterizations and Smoothness Properties
.......... 93
3.3
The Subdifferential
......................... 107
3.4
The
Hardy-Littłewood-Półya
Inequality
............. 109
3.5
Means and Their Inequalities
................... 115
VI
3.5.1
Quasiarithmetic
Means
.................. 116
3.5.2
Rado s and Popoviciu s Inequality for Means
...... 119
3.5.3
Ky Fan s and the Wang-Wang Inequality
........ 121
3.6
Convexity With Respect to Means
................ 124
3.7
The Hermite-Hadamard Inequality
................ 136
3.8
Comments
.............................. 141
Convex Functions on Topological Linear Spaces
147
4.1
Continuity of Convex Functions on Topological Linear Spaces
. 147
4.2
Directional Derivatives and the Algebraic Subdifferential
.... 153
4.3
The Subdifferential
......................... 159
4.4
Differentiability and How to Recognize a Convex Function of
Several Variables
.......................... 163
4.5
The Hermite-Hadamard Inequality for Functions of a Vector
Variable
............................... 177
4.6
Convex Optimization
........................ 193
4.7
The
Fenchel
Conjugate
....................... 198
4.8
The
Fenchel Biconjugate...................... 206
Part III: Families of Convex Functions
Singularities of Families of Extended Real-Valued Functions
211
5.1
Singularities of Families of Extended Real-Valued Functions on
Topological Spaces
.........................211
5.2
Singularities of Families of Extended Real-Valued Functions on
Topological Linear Spaces
.....................215
5.3
Singularities of Families of Functions on Quasinormed Spaces
. 222
Applications of the Singularities of Families of Real-Valued
Functions
227
6.1
Topological Properties of Certain Classes of Functions of Gen¬
eralized Bounded Variation
....................227
6.1.1
Functions of Bounded
λ-
Variation of Order
ρ
......227
6.1.2
Functions of Bounded mth Variation of Order
ρ
.... 238
6.2
Topological Properties of Certain Classes of Linear Operators
. 242
6.3
Topological Properties of Certain Classes of Bounded Sequences
of Numbers
.............................244
Vil
7
Singularities of Families of Convex Vector-Valued Functions
249
7.1
Singularities of Families of Set-Valued Functions
......... 249
7.2
Singularities of Families of s-Convex Vector-Valued Functions
on Topological Linear Spaces
................... 253
7.2.1
Preordered Topological Linear Spaces and s-Convex
Vector-Valued Functions
.................. 253
7.2.2
Singularities of Families of s-Convex Vector-Valued
Functions on Topological Linear Spaces
......... 257
7.3
Singularities of Families of Convex Vector-Valued Functions on
Ultrabarrelled
and Barrelled Spaces
............... 260
7.3.1
Singularities of Families of Linear Functions
....... 261
7.3.2
Singularities of Families of Convex Functions
...... 263
8
Equicontinuity and Holder Equicontinuity of Families of
s-Convex Functions
273
8.1
Equicontinuity and Holder Equicontinuity of Families of
s-Convex Vector-Valued Functions
................273
8.1.1
Characterization of Holder Equicontinuity by Means of
Pseudonorms
........................273
8.1.2
Equicontinuity of Families of s-Convex Functions
at a Point
..........................277
8.1.3
Equicontinuity of Families of s-Convex Functions
on a Set
...........................284
8.2
Equicontinuity and Holder Equicontinuity of Families of
s-Convex Set-Valued Functions
..................287
Part IV: Functional Equations Related to Convex Functions
9
Gamma
-Туре
Functional Equations
301
9.1
Log-Convex Solutions to the Functional Equation
f(x+l)=g{x)f(x)
........................ 301
9.1.1
Uniqueness of Solutions
.................. 302
9.1.2
Existence of a Unique Log-Convex Solution
....... 304
9.1.3
Г-Туре
Functions and Their Multiplication Formula
. . 307
9.1.4
Asymptotic Behaviour of
Г-Туре
Functions
....... 309
9.2
Log-Convex Solutions of the Second Order to the Functional
Equation f(x
+ 1) =
g(x)f(x)
................... 310
9.2.1
An Asymptotic Condition
................. 311
9.2.2
A Uniqueness Result
.................... 313
9.2.3
An Existence and Uniqueness Result
........... 315
Vlil
9.2.4
C?-Type
Functions and Their Multiplication Formula
. . 320
9.3
Hyers-Ulam-Rassias Stability of the Functional Equation
f(tp(x))=g(x)f(x) + h(x)
.....................323
9.4
Stability in the Sense of R.
Ger
of the Functional Equation
f{<p{x))=g(x)f(x)
......................... 337
9.5
Hyers-Ulam-Rassias Stability of a Linear Functional Equation
With Constant Coefficients
.................... 340
9.6
Comments
.............................. 345
10
Popoviciu s Functional Equation
347
10.1
The General Solution
........................ 347
10.2
Hyers-Ulam-Rassias Stability
................... 354
10.2.1
Stability of Popoviciu s Functional Equation
....... 355
10.2.2
Stability of the Quadratic Counterpart of Popoviciu s
Functional Equation
.................... 363
10.3
Comments
.............................. 370
Bibliography
371
Index
387
|
| any_adam_object | 1 |
| author | Breckner, Wolfgang W. |
| author_facet | Breckner, Wolfgang W. |
| author_role | aut |
| author_sort | Breckner, Wolfgang W. |
| author_variant | w w b ww wwb |
| building | Verbundindex |
| bvnumber | BV036754322 |
| classification_rvk | SK 420 |
| ctrlnum | (OCoLC)705943299 (DE-599)BVBBV036754322 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV036754322 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:47:21Z |
| institution | BVB |
| isbn | 9789736107177 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020671522 |
| oclc_num | 705943299 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XIV, 390 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Presa Universitară Clujeană |
| record_format | marc |
| spelling | Breckner, Wolfgang W. Verfasser aut Convex functions and related functional equations selected topics Wolfgang W. Breckner ; Tiberiu Trif Cluj-Napoca Presa Universitară Clujeană 2008 XIV, 390 S. txt rdacontent n rdamedia nc rdacarrier Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf Funktionalgleichung (DE-588)4018923-5 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 s Funktionalgleichung (DE-588)4018923-5 s DE-604 Trif, Tiberiu Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020671522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Breckner, Wolfgang W. Convex functions and related functional equations selected topics Konvexe Funktion (DE-588)4139679-0 gnd Funktionalgleichung (DE-588)4018923-5 gnd |
| subject_GND | (DE-588)4139679-0 (DE-588)4018923-5 |
| title | Convex functions and related functional equations selected topics |
| title_auth | Convex functions and related functional equations selected topics |
| title_exact_search | Convex functions and related functional equations selected topics |
| title_full | Convex functions and related functional equations selected topics Wolfgang W. Breckner ; Tiberiu Trif |
| title_fullStr | Convex functions and related functional equations selected topics Wolfgang W. Breckner ; Tiberiu Trif |
| title_full_unstemmed | Convex functions and related functional equations selected topics Wolfgang W. Breckner ; Tiberiu Trif |
| title_short | Convex functions and related functional equations |
| title_sort | convex functions and related functional equations selected topics |
| title_sub | selected topics |
| topic | Konvexe Funktion (DE-588)4139679-0 gnd Funktionalgleichung (DE-588)4018923-5 gnd |
| topic_facet | Konvexe Funktion Funktionalgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020671522&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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