A Differential Inequality for the Distance Function in Normed Linear Spaces.
Ray Redheffer, Wolfgang Walter (1974)
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Ray Redheffer, Wolfgang Walter (1974)
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V. KLEE (1959/1960)
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A.L. Brown (1987/88)
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Surjit Singh Khurana (1975)
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W.A.J. LUXEMBURG, A.C. ZAANEN (1965/66)
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Gilles Fournier, Heinz-Otto Peitgen (1977)
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G. Godini (1987/88)
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Makeev, V.V. (2005)
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I. SINGER (1965)
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We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.