On an -Birkhoff orthogonality.
Chmieliński, Jacek (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Chmieliński, Jacek (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Saadati, R., Adibi, H. (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Miličić, Pavle M. (2002)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Serb, Ioan (1999)
Mathematica Pannonica
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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.
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...
Salah, Mecheri (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Singh, Vinai K., Kumar, Santosh (2009)
General Mathematics
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Javier Alonso, Carlos Benítez (1989)
Extracta Mathematicae
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Hiroyasu Mizuguchi, Kichi-Suke Saito, Ryotaro Tanaka (2013)
Open Mathematics
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Recently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the Dunkl-Williams constant DW(X) of a normed linear space X. In this paper we present some characterizations of this constant. As an application, we calculate DW(ℓ2-ℓ∞) in the Day-James space ℓ2-ℓ∞.
Kapoor, O.P., Prasad, Jagadish (1984)
Publications de l'Institut Mathématique. Nouvelle Série
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Jebril, Iqbal H., Ali, Radhi Ibrahim M. (2003)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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