| Title:
|
New extension of the variational McShane integral of vector-valued functions (English) |
| Author:
|
Kaliaj, Sokol Bush |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
137-148 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset $G$ of $m$-dimensional Euclidean space $\mathbb {R}^{m}$. It is a "natural" extension of the variational McShane integral (the strong McShane integral) from $m$-dimensional closed non-degenerate intervals to open and bounded subsets of $\mathbb {R}^{m}$. We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our integral to the study of the variational McShane integral. As an application, a full descriptive characterization of the Hake-variational McShane integral is presented in terms of the cubic derivative. (English) |
| Keyword:
|
Hake-variational McShane integral |
| Keyword:
|
variational McShane integral |
| Keyword:
|
Banach space |
| Keyword:
|
$m$-dimensional Euclidean space |
| MSC:
|
28B05 |
| MSC:
|
46B25 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 07088841 |
| idMR:
|
MR3974183 |
| DOI:
|
10.21136/MB.2018.0114-17 |
| . |
| Date available:
|
2019-06-21T11:32:32Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147755 |
| . |
| Reference:
|
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| Reference:
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| . |
