相关论文: Refined Young inequalities with Specht's ratio

We study the symmetrized noncommutative arithmetic geometric mean inequality introduced(AGM) by Recht and R\'{e} $$ \|\frac{(n-d)!}{n!}\sum\limits_{{ j_1,...,j_d \mbox{ different}}…

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

Let $\mu$ be a non-negative Borel measure on $R^d$ satisfying that the measure of a cube in $R^d$ is smaller than the length of its side raised to the $n$-th power, $0<n\leq d$. In this article we study the class of weights related to the…

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, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present \begin{align*}…

Let $\mathcal{A}$ be a unital $JB$-algebra and $A,~B\in\mathcal{A}$, we extend the weighted geometric mean $A\sharp_r B$, from $r\in [0,1]$ to $r\in (-1, 0)\cup(1, 2)$. We will notice that many results will be reversed when the domain of…

Resolvent average and weighted \(\mathcal{A}\sharp \mathcal{H}\)-mean have been defined recently for positive definite matrices. Since the class of accretive matrices provides a general framework for addressing certain known results on…

We present a general refinement of the Cauchy-Schwarz inequality over complete inner product spaces and show that it can be of interest for some statistical applications. This generalizes and simplifies previous results on the same subject.

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $\R^d$, $d \geq 2$. In particular, we derive upper bounds on Riesz means of order $\sigma \geq 3/2$, that improve the sharp Berezin inequality…

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

A mixed arithmetic-mean, geometric-mean inequality was conjectured by F. Holland and proved by K. Kedlaya. In this note, we prove a mixed arithmetic-mean, harmonic-mean inequality and a mixed geometric-mean, harmonic-mean, and a more…

In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved.

We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…

It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…

Let $\mathscr{A}$ be a unital $C^*$-algebra with unit $e$ and let $\nu\in(0, 1)$. We introduce the concept of the $\nu$-weighted contraharmonic of two positive definite elements $a$ and $b$ of $\mathscr{A}$ by \begin{align*} {C}_{\nu}(a,…

The main goal of this article is to present new inequalities for the spectral geometric mean $A\natural_t B$ of two positive definite operators $A, B$ on a Hilbert space. The obtained results complement many known inequalities for the…

In this article, we prove that convex functions and log-convex functions obey certain general refinements that lead to several refinements and reverses of well known inequalities for matrices, including Young's inequality, Heinz inequality,…

The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted…

In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.