| Title:
|
Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference (English) |
| Author:
|
Alsina, C. |
| Author:
|
Guijarro, P. |
| Author:
|
Tomás, M. S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
233-239 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define the radius of the inscribed and circumscribed circumferences in a triangle located in a real normed space and we obtain new characterizations of inner product spaces. (English) |
| Keyword:
|
inner product space |
| Keyword:
|
norm derivative $\rho ^{\prime }_{\pm }$ |
| Keyword:
|
bisectrix |
| Keyword:
|
perpendicular bisector |
| MSC:
|
46B20 |
| MSC:
|
46C05 |
| MSC:
|
46C15 |
| MSC:
|
51M04 |
| MSC:
|
52A10 |
| idZBL:
|
Zbl 0909.46020 |
| idMR:
|
MR1421858 |
| . |
| Date available:
|
2008-06-06T21:31:13Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107576 |
| . |
| Reference:
|
[1] Alsina, C., Guijarro, P. and Tom s, M. S.: On heights in real normed spaces and characterizations of inner product structures.Jour. Int. Math. & Comp. Sci. Vol. 6, N. 2, 151-159 (1993). MR 1239743 |
| Reference:
|
[2] Alsina, C., Guijarro, P. and Tom s, M. S.: A characterization of inner product spaces based on a property of height’s transform.Arch. Math. 61 (1993), 560-566. MR 1254068 |
| Reference:
|
[3] Alsina, C. and Garcia Roig, J. L.: On a functional equation characterizing inner product spaces.Publ. Math. Debrecen 39 (1991), 299-304. MR 1154261 |
| Reference:
|
[4] Alsina, C., Guijarro, P. and Tom s, M. S.: Some remarkable lines of a triangle in real normed spaces and characterizations of inner product structures.(Accepted for publication in Aequationes Mathematicae). |
| Reference:
|
[5] Amir, D.: Characterization of inner product spaces.Basel-Boston (1986). Zbl 0384.46007, MR 0941812 |
| Reference:
|
[6] James, R. C.: Inner products in normed linear spaces.Bull. Amer. Math. Soc. Vol. 53 (1947), 559-566. Zbl 0041.43701, MR 0021242 |
| Reference:
|
[7] Tapia, R. A.: A characterization of inner product spaces.Proc. Amer. Math. Soc. Vol. 41 (1973), 569-574. Zbl 0286.46025, MR 0341041 |
| . |
