| Title:
|
Two mappings related to semi-inner products and their applications in geometry of normed linear spaces (English) |
| Author:
|
Dragomir, S. S. |
| Author:
|
Koliha, J. J. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
45 |
| Issue:
|
5 |
| Year:
|
2000 |
| Pages:
|
337-355 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce two mappings associated with the lower and upper semi-inner product $(\cdot ,\cdot )_i$ and $(\cdot ,\cdot )_s$ and with semi-inner products $[\cdot ,\cdot ]$ (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants. (English) |
| Keyword:
|
lower and upper semi-inner product |
| Keyword:
|
semi-inner products |
| Keyword:
|
Schwarz inequality |
| Keyword:
|
smooth normed spaces |
| Keyword:
|
Birkhoff orthogonality |
| Keyword:
|
best approximants |
| MSC:
|
41A50 |
| MSC:
|
46B20 |
| MSC:
|
46B99 |
| MSC:
|
46C50 |
| MSC:
|
46C99 |
| idZBL:
|
Zbl 0996.46007 |
| idMR:
|
MR1777019 |
| DOI:
|
10.1023/A:1022268627299 |
| . |
| Date available:
|
2009-09-22T18:04:25Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134444 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
