Results 11 to 20 of about 402 (231)
The Goldstine Theorem for asymmetric normed linear spaces
Topology and its Applications, 2009 If \(X\) is a linear space, then a function \(q: X\to\mathbb{R}^+\) is called an asymmetric norm on \(X\) if for all \(x,y\in X\) and \(r\in \mathbb{R}^+\), \(x= 0\) if and only if \(q(x)= q(-x)= 0\), \(q(rx)= rq(x)\) and \(q(x+ y)= q(x)+ q(y)\). It follows that the function \(q^s: X\to\mathbb{R}\) defined by \(d^s(x)= \max(q(x), q(-x))\) is a norm on \
García-Raffi, L.M. +2 more
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Local compactness in right bounded asymmetric normed spaces [PDF]
Quaestiones Mathematicae, 2017 We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, as compactness and strong compactness. In contrast with some results found in the existing literature, we show that not all right bounded asymmetric norms have compact closed
Jonard Pérez,Natalia +1 more
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The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces
MathematicsRoughly speaking, Ekeland’s Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324–353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space.
Ştefan Cobzaş
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Asymmetric norms and optimal distance points in linear spaces
Topology and its Applications, 2008 Let \(X\) be a real vector space. A mapping \(q : X \to [0, \infty)\) is called an asymmetric norm and \((X,q)\) an asymmetric normed space if it satisfies, for all \(x,y \in X\) and \(a \geq 0\), the conditions \(q(a x) = a q(x),\; q(x+y) \leq q(x) + q(y)\), and \(q(x) = q(-x) = 0\) only for \(x = 0\).
García Raffi, L.M. +1 more
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Extremal function pairs in asymmetric normed linear spaces
Topology and its Applications, 2014 This is a continuation of the previous joint paper by the author, \textit{E. Kemajou} et al. [Topology Appl. 159, No. 9, 2463--2475 (2012; Zbl 1245.54023)] on hyperconvexity on \(T_0\)-quasi-metric spaces. Sample results: Every point in the \(q\)-hyperconvex hull of an asymmertic normed linear space is extremal.
Olela Otafudu, Olivier
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Asymmetric free spaces and canonical asymmetrizations [PDF]
, 2023 A construction analogous to that of Godefroy-Kalton for metric spaces allows to embed isometrically, in a canonical way, every quasi-metric space (X, d) to an asymmetric normed space Fa(X, d), its semi-Lipschitz free space.
Daniilidis, Aris; orcid:
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Hahn-Banach type extension results for linear operators on asymmetric normed spaces
We present some results related to Hahn-Banach extension theorem for linear operators on asymmetric normed spaces. L. Nachbin, Trans. Amer. Math. Soc. 68 (1950), proved that a Banach space has the extension property for linear operators (a property also called injectivity) if and only if it has the Binary Intersection Property (BIP), meaning that every
Cobzaş, S.
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Compactness in asymmetric normed spaces
Topology and its Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alegre, C. +3 more
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Asymmetric Norms and the dual complexity spaces. [PDF]
, 2015 Desde el punto de vista de la Ciencia de la Computación, un avance reciente lo ha constituido el establecimiento de un modelo matemático que da cuenta de la distancia entre algoritmos y programas, cuando estos son analizados desde la óptica de la complejidad computacional, entendiendo por complejidad, por ejemplo, la medida del tiempo de computación.
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Best approximation in spaces with asymmetric norm
Journal of Numerical Analysis and Approximation Theory, 2006 In this paper we shall present some results on spaces with asymmetric seminorms, with emphasis on best approximation problems in such spaces.
Ştefan Cobzaş, Costică Mustăţa
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