On the definition of a probalistic normed space.
C. Alsina, A. Sklar, B. Schweizer (1993)
Aequationes mathematicae
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C. Alsina, A. Sklar, B. Schweizer (1993)
Aequationes mathematicae
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C. Alsina, A. Sklar, B. Schweizer (1992)
Aequationes mathematicae
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Detlef Laugwitz (1993)
Aequationes mathematicae
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Makeev, V.V. (2005)
Journal of Mathematical Sciences (New York)
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C.-S. Lin (2005)
Colloquium Mathematicae
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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.
Braß, Peter (1999)
Beiträge zur Algebra und Geometrie
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Carlos Benítez Rodríguez (1989)
Revista Matemática de la Universidad Complutense de Madrid
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Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized...