Rectangular modulus and geometric properties of normed spaces.
Serb, Ioan (1999)
Mathematica Pannonica
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Displaying similar documents to “On minimal points”
Rectangular modulus and geometric properties of normed spaces.
(P)-sets, quasipolyhedra and stability
Jiří Reif (1979)
Commentationes Mathematicae Universitatis Carolinae
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On strictly convex and strictly 2-convex 2-normed spaces. II.
Lin, C.-S. (1992)
International Journal of Mathematics and Mathematical Sciences
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Geometric properties of normed spaces and estimates for rectangular modulus.
Şerb, Ioan (2001)
Mathematica Pannonica
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A universal modulus for normed spaces
Carlos Benítez, Krzysztof Przesławski, David Yost (1998)
Studia Mathematica
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We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.
Mapping in normed linear spaces and characterization of orthogonality problem of best approximations in 2-norm.
Singh, Vinai K., Kumar, Santosh (2009)
General Mathematics
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On the calculation of the Dunkl-Williams constant of normed linear spaces
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∞.