| Title:
|
On vector functions of bounded convexity (English) |
| Author:
|
Veselý, Libor |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
321-335 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a normed linear space. We investigate properties of vector functions $F\colon [a,b] \to X$ of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity $K_a^b F$ is equal to the variation of $F'_+$ on $[a,b)$. As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping. (English) |
| Keyword:
|
bounded convexity |
| Keyword:
|
delta-convex mapping |
| Keyword:
|
bounded variation |
| Keyword:
|
Banach space |
| MSC:
|
26A99 |
| MSC:
|
47H99 |
| idZBL:
|
Zbl 1199.47242 |
| idMR:
|
MR2494785 |
| DOI:
|
10.21136/MB.2008.140621 |
| . |
| Date available:
|
2010-07-20T17:34:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140621 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| . |
