Related papers: Some refinements of classical inequalities

In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of $v$, namely $v\in \mathbb{R}$. These modified inequalities are used to establish corresponding operator inequalities on a…

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens's type.

In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence,…

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…

In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…

In this article we present some new comparisons between the Heinz and Heron operator means, which improve some recent results known from the literature. We derive some refinements of these inequalities for unitarily invariant norms with the…

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.

The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…

We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…

It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental Arithmetic mean - Geometric mean - Harmonic mean inequality in terms of the means and variance of positive real…

A refinement of the Hardy inequality has been presented by use of superquadratic function.

We establish upper bounds for the convolution operator acting between interpolation spaces. This will provide several examples of Young Inequalities in different families of function spaces. We use this result to prove a bilinear…

We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{{n=1}}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{{n=1}}^{\infty }\left({\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}\right)^{2},…

We develop a new framework for the Jensen-type inequalities that allows us to deal with functions not necessarily convex and Borel measures not necessarily positive.

In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…

We prove a sharp integral inequality that generalizes the well known Hardy type integral inequality for negative exponents. We also give sharp applications in two directions for Muckenhoupt weights on R. This work refines the results that…

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.

In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…

A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…