Related papers: A refinement of the arithmetic-geometric mean ineq…
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.
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmetic-geometric mean.
We extend a result of Holland on a mixed arithmetic-geometric mean inequality.
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.
In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the H\"{o}lder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…
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.
We consider the $p$-generalized arithmetic-geometric mean inequality for vectors chosen randomly from the $\ell_p^n$-ball in $\mathbb{R}^n$. In this setting the inequality can be improved or reversed up to a respective scalar constant with…
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
The classical AM-GM inequality has been generalized in a number of ways. Generalizations which incorporate variance appear to be the most useful in economics and finance, as well as mathematically natural. Previous work leaves unanswered…
A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights
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…
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between…
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
In this note we revisit the classical geometric-arithmetic mean inequality and find a formula for the difference of the arithmetic and the geometric means of given $n\in\mathbb N$ nonnegative numbers $x_1,x_2,\dots,x_n$. The formula yields…
Inspired by the recent work by R.Pal et al., we give further refined inequalities for a convex Riemann integrable function, applying the standard Hermite-Hadamard inequality. Our approach is different from their one in \cite{PSMA2016}. As…
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…