Three proofs of Minkowski's second inequality in the geometry of numbers [PDF]
Journal of the Australian Mathematical Society, 1965 Let K be a bounded, open convex set in euclidean n-space Rn, symmetric in the origin 0. Further let L be a lattice in Rn containing 0 and put extended over all positive real numbers ui for which uiK contains i linearly independent points of L. Denote the
R. P. Bambah +2 more
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An elementary proof of Minkowski's second inequality [PDF]
Journal of the Australian Mathematical Society, 1969 Let K be an open convex domain in n-dimensional Euclidean space, symmetric about the origin O, and of finite Jordan content (volume) V. With K are associated n positive constants λ1, λ2,…,λn, the ‘successive minima of K’ and n linearly independent ...
I. Danicic
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Minkowski's fundamental inequality for reduced positive quadratic forms [PDF]
Journal of the Australian Mathematical Society, 1978 Forms which are reduced in the sense of Minkowski satisfy the “fundamental inequality” a11a22 hellipann≤λnD; the best possible value of λn is known for n≤5.
Edwin Barnes
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A generalisation of Minkowski's second inequality in the geometry of numbers [PDF]
Journal of the Australian Mathematical Society, 1966 Let K be a bounded open convex set in euclidean n-space Rn symmetric in the origin 0. Further let L be a discrete point set in Rn containing 0 and at least n linearly independent points of Rn.
Alan C. Woods
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Novel versions of Hölder's-Like and related inequalities with newly defined LP space, and their applications over fuzzy domain [PDF]
HeliyonIt is widely recognized that fuzzy number theory relies on the characteristic function. However, within the fuzzy realm, the characteristic function transforms into a membership function contingent upon the interval [0,1].
Xiangting Shi +4 more
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Minkowski's fundamental inequality for reduced positive quadratic forms(II) [PDF]
Journal of the Australian Mathematical Society, 1979 A convex polytope D (α) was defined in Barnes (1978) as the set of Minkowski-reduced forms with prescribed diagonal coefficients α1, α2,…αn. A local minimum of the determinant D(f) over D(α) must occur at a vertex of D(α).
Edwin Barnes
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Some new generalizations of reversed Minkowski's inequality for several functions via time scales
AIMS MathematicsIn this paper, we introduce novel extensions of the reversed Minkowski inequality for various functions defined on time scales. Our approach involves the application of Jensen's and Hölder's inequalities on time scales.
Elkhateeb S. Aly +3 more
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A converse of Minkowski's inequality
Discrete Mathematics, 2000 AbstractThe following converse of the classical Minkowski inequality was proved by H.
Horst Alzer, Stephan Ruscheweyh
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Continuous Sharpening of Hölder's and Minkowski's Inequalities [PDF]
, 2005 Some properties of functions which in special cases lead to sharpening of Holder’s and other interesting inequalities are proved. Results analogue to theorems leading to reverse Holder’s inequality are presented. Mathematics subject classification (2000):
Shoshana Abramovich +2 more
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An Improvement of an Inequality of Minkowski. [PDF]
Proc Natl Acad Sci U S A, 1951 Ankeny NC.
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