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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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THE EXISTENCE OF EXTREME POINTS OF COMPACT CONVEX SETS IN ASYMMETRIC CONE NORMED SPACES
Journal of Mathematical AnalysisOptimization has been one of the most popular applications in real-world problems from the past into the present. The concept of extreme points plays a vital role in optimization, and the existence of extreme points of compact convex subsets of a locally convex (Hausdorff) vector space can be obtained from the Krein-Milman theorem.
WASIN SUPAKUL, WUTIPHOL SINTUNAVARAT
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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, 2006Jesus Rodríguez-López +1 more
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Any two-dimensional Normed space is a generalized Day-James space
Journal of Inequalities and Applications, 2011Javier Alonso
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A note on the definition of a generalized fuzzy normed space
Fuzzy Sets and Systems, 2014Dorel Mihet
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Equilateral simplices in a four-dimensional normed space
Journal of Mathematical Sciences, 2007V V Makeev
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Completeness of fuzzy normed linear space of all weakly fuzzy bounded linear operators
Fuzzy Sets and Systems, 2014exaly