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Alternative reverse inequalities for Young's inequality [PDF]
Journal of Mathematical Inequalities, Vol.5(2011), pp.595-600, 2011 Two reverse inequalities for Young's inequality were shown by M. Tominaga, using Specht ratio. In this short paper, we show alternative reverse inequalities for Young's inequality without using Specht ratio.
arxiv +1 more source
Improvements and generalizations of two Hardy type inequalities and their applications to the Rellich type inequalities [PDF]
arXiv, 2021 We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with best constants. Besides, we improve two Rellich type inequalities by using the improved Hardy type inequality.
arxiv
On some tensor inequalities based on the t-product [PDF]
arXiv, 2021 In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The well-known arithmetic-geometric mean inequality, H{\" o}lder inequality, and Minkowski inequality are generalized to
arxiv
Concentration Inequalities for Markov Jump Processes [PDF]
arXiv, 2022 We derive concentration inequalities for empirical means $\frac{1}{t} \int_0^t f(X_s) ds$ where $X_s$ is an irreducible Markov jump process on a finite state space and $f$ some observable. Using a Feynman-Kac semigroup we first derive a general concentration inequality. Then, based on this inequality we derive further concentration inequalities. Hereby
arxiv
Analytic aspects of the dilation inequality for symmetric convex sets in Euclidean spaces [PDF]
arXiv, 2023 We discuss an analytic form of the dilation inequality for symmetric convex sets in Euclidean spaces, which is a counterpart of analytic aspects of Cheeger's isoperimetric inequality. We show that the dilation inequality for symmetric convex sets is equivalent to a certain bound of the relative entropy for symmetric quasi-convex functions, which is ...
arxiv
On classical inequalities of trigonometric and hyperbolic functions [PDF]
arXiv, 2014 This article is the collection of the six research papers, recently written by the authors. In these papers authors refine the inequalities of trigonometric and hyperbolic functions such as Adamovic-Mitrinovic inequality, Cusa-Huygens inequality, Lazarevic inequality, Huygens inequality, Jordan's inequality, Carlson's inequality, Wilker's inequality ...
arxiv
On some inequalities for Gaussian measures [PDF]
Proceedings of the ICM, Beijing 2002, vol. 2, 813--822, 2003 We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.
arxiv
Operator inequalities via the triangle inequality [PDF]
arXiv, 2022 This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator applications include numerical radius inequalities and operator mean inequalities.
arxiv
Inequalities of Levin-Stečkin, Clausing and Chebyshev revisited [PDF]
arXiv, 2016 We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .
arxiv
Entropy Inequalities and Gaussian Comparisons [PDF]
arXiv, 2022 We establish a general class of entropy inequalities that take the concise form of Gaussian comparisons. The main result unifies many classical and recent results, including the Shannon-Stam inequality, the Brunn-Minkowski inequality, the Zamir-Feder inequality, the Brascamp-Lieb and Barthe inequalities, the Anantharam-Jog-Nair inequality, and others.
arxiv