Characterizations of inner product spaces through an isosceles trapezoid property
Claudi Alsina; P. Cruells; M. S. Tomás
Archivum Mathematicum (1999)
- Volume: 035, Issue: 1, page 21-27
- ISSN: 0044-8753
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topAlsina, Claudi, Cruells, P., and Tomás, M. S.. "Characterizations of inner product spaces through an isosceles trapezoid property." Archivum Mathematicum 035.1 (1999): 21-27. <http://eudml.org/doc/248350>.
@article{Alsina1999,
abstract = {Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.},
author = {Alsina, Claudi, Cruells, P., Tomás, M. S.},
journal = {Archivum Mathematicum},
keywords = {inner product space; norm derivative $\rho ^\{\prime \}_\{\pm \}$; heights; inner product space; heights},
language = {eng},
number = {1},
pages = {21-27},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Characterizations of inner product spaces through an isosceles trapezoid property},
url = {http://eudml.org/doc/248350},
volume = {035},
year = {1999},
}
TY - JOUR
AU - Alsina, Claudi
AU - Cruells, P.
AU - Tomás, M. S.
TI - Characterizations of inner product spaces through an isosceles trapezoid property
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 1
SP - 21
EP - 27
AB - Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.
LA - eng
KW - inner product space; norm derivative $\rho ^{\prime }_{\pm }$; heights; inner product space; heights
UR - http://eudml.org/doc/248350
ER -
References
top- Alsina C., Guijarro P., Tomás M. S., On heights in real normed spaces and characterizations of inner product structures, Jour. Int. Math. & Comp. Sci. Vol. 6, N. 2(1993), 151-159. (1993) Zbl0816.46017MR1239743
- Alsina C., Guijarro P., Tomás M. S., A characterization of inner product spaces based on a property of height’s transform, Archiv der Mathematik Vol. 61(1993), 560-566. (1993) MR1254068
- Alsina C., Cruells P., Tomás M. S., Isosceles Trapezoids, Norms and Inner Products, Archiv der Mathematik (1999) (1999) Zbl0928.46010MR1671283
- Amir D., Characterizations of inner product spaces, Birkhäuser Verlag (1986). (1986) Zbl0617.46030MR0897527
- Suzuki F., A Certain Property of an Isosceles Trapezoid and its Application to Chain Circle Problems, Mathematics Magazine Vol. 8, N. 2, pp 136-145 (1995). (1995) Zbl0877.51017MR1333815
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