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inner product space; norm derivative $\rho ^{\prime }_{\pm }$; heights
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.
[1] 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. MR 1239743 | Zbl 0816.46017
[2] 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. MR 1254068
[3] Alsina C., Cruells P., Tomás M. S.: Isosceles Trapezoids, Norms and Inner Products. Archiv der Mathematik (1999) MR 1671283 | Zbl 0928.46010
[4] Amir D.: Characterizations of inner product spaces. Birkhäuser Verlag (1986). MR 0897527 | Zbl 0617.46030
[5] 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). MR 1333815 | Zbl 0877.51017
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