Related papers: A note on the triangle inequality for the Jaccard …

In this paper, a monotonicity property for the quotient of two Jacobi's theta functions with respect to the modulus $k$ is proved.

In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.

When dealing with certain mathematical problems, it is sometimes necessary to show that some function induces a metric on a certain space. When this function is not a well renowned example of a distance, one has to develop very particular…

A note that points out the possibility to have p<1 in Sobolev type of inequalities by a use of the momomial structure of polynomials or power series. The proof is simple: Triangle angle inequality p*>1, monomial estimate from p* to exponent…

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the authors verify…

In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)

We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Tur\'{a}n type inequalities and bounds for ratios of modified Lommel functions of the first…

We present several sharp upper bounds and some extension for product operators. Among other inequalities, it is shown that if , , are non-negative continuous functions on such that , , then for all non-negative operator monotone decreasing…

Nandakumar asked whether there is a tiling of the plane by pairwise non-congruent triangles of equal area and equal perimeter. Here a weaker result is obtained: there is a tiling of the plane by pairwise non-congruent triangles of equal…

In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, H\"older-Rogers,…

We prove a conjecture of Cuttler et al.~[2011] [A. Cuttler, C. Greene, and M. Skandera; \emph{Inequalities for symmetric means}. European J. Combinatorics, 32(2011), 745--761] on the monotonicity of \emph{normalized Schur functions} under…

We discuss some different results on Sidon-type inequalities and on the space of quasi-continuous functions.

Lebesgue space inequalities are proved for a variant of the triangular Hilbert transform involving curvature. The analysis relies on a crucial trilinear smoothing inequality developed herein, and on bounds for an anisotropic variant of the…

We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of…

First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…

We consider the problem of optimizing the product of the distances from a given point in a triangle to each vertex. There are two possible cases in general. For isosceles triangles, we explicitly show exactly when both cases occur.

We consider a random variable $X$ that takes values in a (possibly infinite-dimensional) topological vector space $\mathcal{X}$. We show that, with respect to an appropriate "normal distance" on $\mathcal{X}$, concentration inequalities for…

First, we consider a nonnegative homogeneous block tri-diagonal matrix and obtain its convergence parameter, where some results in the field of matrix analytic method are extended to the case where block matrices have countably infinite…

We establish a sharp inequality between the blocks of positive partitioned matrices and conjecture a triangle type inequality for contractions: Given three contactions A,B,C, we conjecture that the constant c=3/4 is sharp in the triangle…