Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference

Claudi Alsina; Piedad Guijarro Carranza; M. S. Tomás

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 3, page 233-239
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Alsina, Claudi, Guijarro Carranza, Piedad, and Tomás, M. S.. "Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference." Archivum Mathematicum 032.3 (1996): 233-239. <http://eudml.org/doc/247847>.

@article{Alsina1996,
abstract = {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.},
author = {Alsina, Claudi, Guijarro Carranza, Piedad, Tomás, M. S.},
journal = {Archivum Mathematicum},
keywords = {inner product space; norm derivative $\rho ^\{\prime \}_\{\pm \}$; bisectrix; perpendicular bisector; inner product space; norm derivative; bisectrix; perpendicular bisector; radius of the inscribed circumference; strictly convex real normed spaces},
language = {eng},
number = {3},
pages = {233-239},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference},
url = {http://eudml.org/doc/247847},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Alsina, Claudi
AU - Guijarro Carranza, Piedad
AU - Tomás, M. S.
TI - Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 3
SP - 233
EP - 239
AB - 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.
LA - eng
KW - inner product space; norm derivative $\rho ^{\prime }_{\pm }$; bisectrix; perpendicular bisector; inner product space; norm derivative; bisectrix; perpendicular bisector; radius of the inscribed circumference; strictly convex real normed spaces
UR - http://eudml.org/doc/247847
ER -

References

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  1. On heights in real normed spaces and characterizations of inner product structures, Jour. Int. Math. & Comp. Sci. Vol. 6, N. 2, 151-159 (1993). MR1239743
  2. A characterization of inner product spaces based on a property of height’s transform, Arch. Math. 61 (1993), 560-566. MR1254068
  3. On a functional equation characterizing inner product spaces, Publ. Math. Debrecen 39 (1991), 299-304. MR1154261
  4. Some remarkable lines of a triangle in real normed spaces and characterizations of inner product structures, (Accepted for publication in Aequationes Mathematicae). 
  5. Characterization of inner product spaces, Basel-Boston (1986). Zbl0384.46007MR0941812
  6. Inner products in normed linear spaces, Bull. Amer. Math. Soc. Vol. 53 (1947), 559-566. Zbl0041.43701MR0021242
  7. A characterization of inner product spaces, Proc. Amer. Math. Soc. Vol. 41 (1973), 569-574. Zbl0286.46025MR0341041

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