Related papers: An inequality for t-geometric means
The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all…
From geometrical point of view, Eve (2003) studied seven means. These means are Harmonic, Geometric, Arithmetic, Heronian, Contra-harmonic, Root-mean square and Centroidal mean. We have considered for the first time a new measure calling…
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian measures. Unlike in the classical Brunn-Minkowski theory, the…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar…
We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
For $n$ positive numbers ($a_k$, $1\leq k \leq n$), enhanced inequalities about the arithmetic mean ($A_n \equiv \frac{\sum_ka_k}{n}$) and the geometric mean ($G_n\equiv \sqrt[n]{\Pi_ka_k}$) are found if some numbers are known, namely,…
In this note we prove Jensen-type inequality for certain non-convex functions. We apply our idea to prove some inequalities which were suggested at some high-level math olympiades.
It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality…
We present here several versions of the Grothendieck inequality over the skew field of quaternions: The first one is the standard Grothendieck inequality for rectangular matrices, and two additional inequalities for self-adjoint matrices,…
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,…
In this work, we improve and refine some numerical radius inequalities. In particular, for all Hilbert space operators $T$, the celebrated Kittaneh inequality reads: \begin{align*} \frac{1}{4}\left\| T^*T + TT^*\right\|\le w^{2 }\left(T…
In this paper we deduce some tight Tur\'an type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some…
This note proves a version of Lubell-Yamamoto-Meshalkin inequality for general product measures.
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
We prove a Harnack inequality for functions which, at points of large gradient, are solutions of elliptic equations with unbounded drift.
We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.