Displaying similar documents to “Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces”

Centralizers for subsets of normed algebras

Bertram Yood (2000)

Studia Mathematica

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Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either c x c - 1 = x for all c ∈ H or s u p ∥ c x c - 1 ∥ : c ∈ H = ∞ . In that case the set of x ∈ A for which the sup is finite is the centralizer of H.

A result on best approximation in p -normed spaces

Abdul Latif (2001)

Archivum Mathematicum

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We study best approximation in p -normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.

Circumradius versus side lengths of triangles in linear normed spaces

Gennadiy Averkov (2007)

Colloquium Mathematicae

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Given a planar convex body B centered at the origin, we denote by ℳ ²(B) the Minkowski plane (i.e., two-dimensional linear normed space) with the unit ball B. For a triangle T in ℳ ²(B) we denote by R B ( T ) the least possible radius of a Minkowskian ball enclosing T. We remark that in the terminology of location science R B ( T ) is the optimum of the minimax location problem with distance induced by B and vertices of T as existing facilities (see, for instance, [HM03] and the references therein)....

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.

Two mappings related to semi-inner products and their applications in geometry of normed linear spaces

Sever Silvestru Dragomir, Jaromír J. Koliha (2000)

Applications of Mathematics

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In this paper we introduce two mappings associated with the lower and upper semi-inner product ( · , · ) i and ( · , · ) s and with semi-inner products [ · , · ] (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants.