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Publikováno v:
Journal of Geometry. 105:1-11
Many characterizations of euclidean spaces (real inner product spaces) among metric spaces have been based on euclidean four point embeddability properties. Related “intrinsic” four point properties have also been used to characterize euclidean o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::79d273082d39f75ea84f8147f34db646
https://doi.org/10.1007/s00022-013-0181-3
https://doi.org/10.1007/s00022-013-0181-3
Publikováno v:
Communications of the Korean Mathematical Society. 20:487-503
Some companions of Gruss inequality in 2-inner product spaces and applications for determinantal integral inequalities are given.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::baa380e0a6b30108843268150fa635ad
https://doi.org/10.4134/ckms.2005.20.3.487
https://doi.org/10.4134/ckms.2005.20.3.487
Autor:
Raymond W. Freese, Edward Z. Andalafte
Publikováno v:
Journal of Geometry. 75:97-105
Generalized euclidean spaces have been characterized among metric spaces by the requirement that each member of certain classes of quadruples of points of the metric space be congruent to a quadruple of points of a euclidean space. The present paper
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ce6cf79a17474d58800fc4424f6e1819
https://doi.org/10.1007/s00022-002-1386-z
https://doi.org/10.1007/s00022-002-1386-z
Autor:
Raymond W. Freese, Edward Z. Andalafte
Publikováno v:
Journal of Geometry. 73:39-48
Many characterizations of euclidean spaces (real inner product spaces) among metric spaces have been based on euclidean four-point embeddability properties. Related "intrinsic" four point properties have also been used to characterize euclidean or hy
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d9cac03720de33467c0d253792c6bb22
https://doi.org/10.1007/s00022-002-8584-6
https://doi.org/10.1007/s00022-002-8584-6
Autor:
Raymond W. Freese, Edward Z. Andalafte
Publikováno v:
Journal of Geometry. 69:1-10
New characterizations of real inner product spaces (euclidean spaces) among metric spaces are obtained from familiar formulas expressing the altitude (height) of a triangle as a function of the lengths of its sides. Other properties related to the al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f66f5f42eef97c665734bc50359de2e1
https://doi.org/10.1007/bf01237469
https://doi.org/10.1007/bf01237469
Autor:
Raymond W. Freese, Edward Z. Andalafte
Publikováno v:
Journal of Geometry. 62:121-128
It is known that the property of additivity of isosceles orthogonality characterizes real inner product spaces among normed linear spaces. In the present paper it is shown that suitably metrized concepts of additivity of metric isosceles orthogonalit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4bf2404a876305c3e8c833f10a9a284b
https://doi.org/10.1007/bf01237604
https://doi.org/10.1007/bf01237604
Publikováno v:
Journal of Geometry. 58:7-14
Characterizations of real inner product spaces among a class of metric spaces have been obtained based on homogeneity of metric pythagorean orthogonality, a metrization of the concept of pythagorean orthogonality as defined in normed linear spaces. I
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::11a1bd7abee268b6dfd47ee8852c6605
https://doi.org/10.1007/bf01222922
https://doi.org/10.1007/bf01222922
Autor:
Raymond W. Freese, Edward Z. Andalafte
Publikováno v:
Journal of Geometry. 56:3-8
It is known that euclidean or hyperbolic spaces are characterized among certain metric spaces by the property of linearity of the equidistant locus of pairs of points. In this paper, this linearity requirement is replaced by the requirement of convex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7b2fbb2af91d71e239cd86f2b6f5cf00
https://doi.org/10.1007/bf01222677
https://doi.org/10.1007/bf01222677