On the definition of a probalistic normed space. (Summary).
C. Alsina, A. Sklar, B. Schweizer (1992)
Aequationes mathematicae
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Displaying similar documents to “On the definition of a probalistic normed space.”
On the definition of a probalistic normed space. (Summary).
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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.
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