Results 211 to 220 of about 1,619,215 (233)
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The Dual Space of an Asymmetric Normed Linear Space
Quaestiones Mathematicae, 2003Given an asymmetric normed linear space ( X , q ), we construct and study its dual space ( X *, q *). In particular, we show that ( x *, q *) is a biBanach semilinear space and prove that ( X , q ) can be identified as a subspace of its bidual by an isometric isomorphism.
L.M. García-Raffi +1 more
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The bicompletion of an asymmetric normed linear space
Acta Mathematica Hungarica, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García-Raffi, L. M. +2 more
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Gradient flows in asymmetric metric spaces
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2022This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and upper gradients
Shin-ichi Ohta, Wei Zhao
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Extensions of asymmetric norms to linear spaces
2011Summary: Let \(M\) be a subset of a (real) linear space that is closed with respect to the sum of vectors and the product by nonnegative scalars. An asymmetric seminorm on \(M\) is a nonnegative and subadditive positively homogeneous function \(q\) defined on \(M\).
Garcìa-Raffi, L.M. +2 more
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The Banach--Mazur Theorem for Spaces with Asymmetric Norm
Mathematical Notes, 2001We establish an analog of the Banach—Mazur theorem for real separable linear spaces with asymmetric norm: every such space can be linearly and isometrically embedded in the space of continuous functions f on the interval [0,1] equipped with the asymmetric norm $$||f|$$
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Separation of Convex Sets and Best Approximation in Spaces with Asymmetric Norm
Quaestiones Mathematicae, 2004No Abstract. Quaestiones Mathematicae Vol.
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The Dual space of an asymmetric normed linear space
2004Given an asymmetric normed linear space (X, q), we construct and study its dual space (X*, q*). In particular, we show that (x*, q*) is a biBanach semilinear space and prove that (X, q) can be identified as a subspace of its bidual by an isometric isomorphism.We also introduce and characterize the so-called weak* topology which is generated in a ...
Garcia-Raffi, L.M. +2 more
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Fuzzy Sets and Systems, 2010
The main results of this paper are characterizations of those paratopological vector spaces that are quasi-metrizable, locally bounded, quasi-metrizable and locally convex, and quasi-normable, respectively, as follows: Let (\(X,\tau\)) be a paratopological vector space.
Carmen Alegre, Salvador Romaguera
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The main results of this paper are characterizations of those paratopological vector spaces that are quasi-metrizable, locally bounded, quasi-metrizable and locally convex, and quasi-normable, respectively, as follows: Let (\(X,\tau\)) be a paratopological vector space.
Carmen Alegre, Salvador Romaguera
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Multidimensional inequalities between distinct metrics in spaces with an asymmetric norm
Sbornik: Mathematics, 1998For \(T^d\) the \(d\)-dimensional torus, \(L_{p,q}(T^d)\) is the space of functions \(f\) on \(T^d\) with \(f^+\in L_p(T^d)\), \(f^-\in L_q(T^d)\) and the norm \(\| f\|_{p,q}=\| f^+\|_p +\| f^-\|_q\). The trigonometric polynomial \(T_n\) of degree \(n_j\) in \(x_j\) satisfies the Jackson-Nikolskij type inequality \[ \| T_n\|_{q_1,q_2}\leq C_ ...
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Izvestiya: Mathematics, 1998
For \(p_1, p_2\in [1, \infty] \) the asymmetric norm of a real-valued measurable function \(f\) on \([-\pi, \pi]\) is defined by \(\|f \|_{p_1,p_2}=\|f^{+}\|_{p_1} + \|f^{-}\|_{p_2}\), where \(f^{+}(t)=\max \{0; f(t)\}\) and \(f^{-}(t)=\max \{0; -f(t)\}\).
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For \(p_1, p_2\in [1, \infty] \) the asymmetric norm of a real-valued measurable function \(f\) on \([-\pi, \pi]\) is defined by \(\|f \|_{p_1,p_2}=\|f^{+}\|_{p_1} + \|f^{-}\|_{p_2}\), where \(f^{+}(t)=\max \{0; f(t)\}\) and \(f^{-}(t)=\max \{0; -f(t)\}\).
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