An Improvement of Minkowski’s Inequality for Sums

In 2012, Sulaiman [Reverses of Minkowski’s, Hölder’s, and Hardy’s integral inequalities, Int. J. Mod. Math. Sci. 1(1) (2012) 14–24] proved integral inequalities concerning reverses of Minkowski’s and Hardy’s inequalities. In 2013, Banyat Sroysang obtained a generalization of the reverse Minkowski’s inequality [More on reverses of Minkowski’s integral inequality, Math. Aeterna 3(7) (2013) 597–600] and the reverse Hardy’s integral inequality [A generalization of some integral inequalities similar to Hardy’s inequality, Math. Aeterna 3(7) (2013) 593–596]. In this article, two results are given. First one is further improvement of the reverse Minkowski inequality and second is further generalization of the integral Hardy inequality.

Download Full-text

Erratum to “Fubini theorem and generalized Minkowski inequality for the pseudo-integral” [Int. J. Approx. Reason. 122 (2020) 9–23]

International Journal of Approximate Reasoning ◽

10.1016/j.ijar.2021.02.005 ◽

2021 ◽

Vol 132 ◽

pp. 127

Author(s):

Deli Zhang ◽

Endre Pap

Keyword(s):

Minkowski Inequality ◽

Fubini Theorem

Download Full-text

Convexity and Minkowski's Inequality

American Mathematical Monthly ◽

10.1080/00029890.2005.11920247 ◽

2005 ◽

Vol 112 (8) ◽

pp. 740-742

Author(s):

Geoffrey Brown

Keyword(s):

Minkowski’S Inequality

Download Full-text

New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces ${L_{\vec{p}}(\mathbb{R}^d)}$

Mathematics ◽

10.3390/math9030227 ◽

2021 ◽

Vol 9 (3) ◽

pp. 227 ◽

Cited By ~ 1

Author(s):

Junjian Zhao ◽

Wei-Shih Du ◽

Yasong Chen

Keyword(s):

Invariant Subspace ◽

Type Inequality ◽

Invariant Subspaces ◽

Minkowski Inequality ◽

Hölder Inequality ◽

Stability Theorem ◽

Mixed Norm ◽

Lebesgue Spaces

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

Download Full-text

Prescribing Centro-Affine Curvature From One Convex Body to Another

International Mathematics Research Notices ◽

10.1093/imrn/rnaa103 ◽

2020 ◽

Author(s):

Alina Stancu

Keyword(s):

Convex Body ◽

Convex Bodies ◽

Minkowski Inequality ◽

Curvature Flow ◽

Constant Volume ◽

Convex Hypersurface ◽

Strictly Convex ◽

Initial Hypersurface ◽

Affine Curvature ◽

Convex Hypersurfaces

Abstract We study a curvature flow on smooth, closed, strictly convex hypersurfaces in $\mathbb{R}^n$, which commutes with the action of $SL(n)$. The flow shrinks the initial hypersurface to a point that, if rescaled to enclose a domain of constant volume, is a smooth, closed, strictly convex hypersurface in $\mathbb{R}^n$ with centro-affine curvature proportional, but not always equal, to the centro-affine curvature of a fixed hypersurface. We outline some consequences of this result for the geometry of convex bodies and the logarithmic Minkowski inequality.

Download Full-text