Related papers: Jensen's Inequalities in Two and Three Dimensions
We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function…
In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert,…
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the…
In this paper, we present an improvement of a large sieve type inequality in high dimensions and discuss its implications on a related problem.
We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.
Yager[5] proposed a transformation for opposing(negating) the occurence of an event that is not certain using the idea that one can oppose the occurence of any uncertain event by allocating its probability among the other outcomes in the…
Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and…
We construct symmetric representations of distributions over two-dimensional plane with given mean values as convex combinations of distributions with supports containing not more than three points and with the same mean values.
The Gaussian product inequality is a long-standing conjecture. In this paper, we investigate the three-dimensional inequality $E[X_1^{2}X_2^{2m_2}X_3^{2m_3}]\ge E[X_1^{2}]E[X_2^{2m_2}]E[X_3^{2m_3}]$ for any centered Gaussian random vector…
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional…
The present survey is devoted to results on Trudinger-Moser inequalities in two dimension. We give a brief overview of the history of these celebrated inequalities and, starting from the geometric problem that motivated Moser's original…
We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number of options for defining the diameter of a convex body that…
We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf, and by Zukowski and Brukner, for the two-dimensional case. Our construction applies for the n parties, two-observables…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
Extensions and generalizations of Alzer's inequality; which is of Wirtinger type are proved. As applications, sharp trapezoid type inequality and sharp bound for the geometric mean are deduced.
We prove an inequality of Hardy type for functions in Triebel-Lizorkin spaces. The distance involved is being measured to a given Ahlfors d-regular set in R^n, with n-1<d<n. As an application of the Hardy inequality, we consider boundedness…