A Characterization of Inner Product Spaces Related to the Skew-Angular Distance
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 549-554.

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A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.
Keywords: triangle inequality, inner product space, angular distance, normed linear space, skew-angular distance.
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H. Dehghan. A Characterization of Inner Product Spaces Related to the Skew-Angular Distance. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 549-554. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a5/

[1] L. Maligranda, “Simple norm inequalities”, Amer. Math. Monthly, 113:3 (2006), 256–260 | DOI | MR | Zbl

[2] L. Maligranda, “Some remarks on the triangle inequality for norms”, Banach J. Math. Anal., 2:2 (2008), 31–41 | MR | Zbl

[3] J. A. Clarkson, “Uniformly convex spaces”, Trans. Amer. Math. Soc., 40:3 (1936), 396–414 | DOI | MR | Zbl

[4] J. L. Massera, J. J. Schäffer, “Linear differential equations and functional analysis, I”, Ann. of Math. (2), 1958, no. 3, 517–573 | DOI | MR | Zbl

[5] C. F. Dunkl, K. S. Williams, “A simple norm inequality”, Amer. Math. Monthly, 71:1 (1964), 53–54 | DOI | MR | Zbl

[6] E. R. Lorch, “On certain implications which characterize Hilbert space”, Ann. of Math. (2), 49:3 (1948), 523–532 | DOI | MR | Zbl