Results 221 to 230 of about 402 (231)

The Banach--Mazur Theorem for Spaces with Asymmetric Norm

Mathematical Notes, 2001
We 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, 2004
No Abstract. Quaestiones Mathematicae Vol.
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Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms

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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Chebyshev sets composed of subspaces in asymmetric normed spaces

Izvestiya: Mathematics
By definition, a Chebyshev set is a set of existence and uniqueness, that is, any point has a unique best approximant from this set. We study properties of Chebyshev sets composed of finitely or infinitely many planes (closed affine subspaces, possibly degenerated to points).
Alimov, Alexey R., Tsar'kov, Igor' G.
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Multidimensional inequalities between distinct metrics in spaces with an asymmetric norm

Sbornik: Mathematics, 1998
For \(T^d\) 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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Fractional derivatives and inequalities for trigonometric polynomials in spaces with asymmetric norms

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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Closedness of bounded convex sets of asymmetric normed linear spaces and the Hausdorff quasi-metric

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2006
Jesus Rodríguez-López, Salvador Romaguera   +1 more
exaly  

I-convergence in probabilistic n-normed space

Soft Computing, 2012
Binod Chandra Tripathy, Mausumi Sen, Tripathy Binod Chandra   +2 more
exaly  

Finite dimensional fuzzy normed linear space

Fuzzy Sets and Systems, 1992
exaly  

The Type of Minimal Branching Geodesics Defines the Norm in a Normed Space

Journal of Mathematical Sciences, 2014
exaly