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Stability of the Logarithmic Brunn–Minkowski Inequality in the Case of Many Hyperplane Symmetries
Studia scientiarum mathematicarum Hungarica (Print), 2021In the case of symmetries with respect to 𝑛 independent linear hyperplanes, a stability versions of the Logarithmic Brunn–Minkowski Inequality and the Logarithmic Minkowski Inequality for convex bodies are established.
K. Boroczky, A. De
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The Minkowski Inequality for Generalized Fractional Integrals
, 2021In this work, the well-known Minkowski inequality is studied, using a generalized fractional integral operator, defined and studied by authors in a previous work. Relationships with known results are established throughout the work and in conclusions.
J. Delgado+3 more
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, 2000
This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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This section is basic for our further considerations and is devoted to those convex sets which lie in finite-dimensional topological vector spaces. As mentioned in the previous section, if E is an arbitrary finite-dimensional (Hausdorff) topological vector space, then E is isomorphic to some Euclidean space R n .
V. V. Buldygin, A. B. Kharazishvili
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Dar’s conjecture and the log–Brunn–Minkowski inequality
, 2016In 1999, Dar conjectured if there is a stronger version of the celebrated Brunn-Minkowski inequality. However, as pointed out by Campi, Gardner, and Gronchi in 2011, this problem seems to be open even for planar o-symmetric convex bodies.
Dongmeng Xi, G. Leng
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Inequalities of GauĂź-Minkowski type
1997An integral version of Ostrowski"s inequality is given. Also, some other generalization of that inequality in connection with Gauss" and Minkowski"s type inequalities are given.
Pearce, Charles E. M.+2 more
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On Reverse Minkowski-Type Inequalities
Mediterranean Journal of Mathematics, 2014In this article, we first establish improvements of the classical Polya-Szego inequality. As applications, we prove reverse Minkowski-type inequalities for convex and star bodies.
Zhao, C, Cheung, WS
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Contemporary Mathematics, 2019
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.
Kriti Goel, R. Gurjar, J. Verma
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In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities of ideals are explained.
Kriti Goel, R. Gurjar, J. Verma
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Properties of Mappings Related to the Minkowski Inequality
Mediterranean Journal of Mathematics, 2010In this paper we obtain properties of several mappings which are arisen from the Minkowski inequality. We investigate superadditivity (subadditivity) and monotonicity of those functions, and give some refinements of the Minkowski inequality and the Holder inequality.
Božidar Ivanković+2 more
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The anisotropic p-capacity and the anisotropic Minkowski inequality
Science China Mathematics, 2021C. Xia, Jiabin Yin
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Convexity and Minkowski's Inequality
The American Mathematical Monthly, 2005(2005). Convexity and Minkowski's Inequality. The American Mathematical Monthly: Vol. 112, No. 8, pp. 740-742.
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