Related papers: A simple proof on the inequality of arithmetic and…
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights
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 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.
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…
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…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, logarithmic means, etc. Inequalities involving logarithmic mean with differences among other means are presented
In the paper, we provide an alternative and united proof of a double inequality for bounding the arithmetic-geometric mean.
We obtain simple proofs of certain inequalites for bivariate means.
We shall give a refinement of the arithmetic-geometric mean inequality.
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 I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
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…
We complement a recent result of S. Furuichi, by showing that the differences $\sum_{i=1}^n \alpha_i x_i - \prod_{i=1}^n x_i^{\alpha_i}$ associated to distinct sequences of weights are comparable, with constants that depend on the smallest…
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…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
As we showed in [3], a geometric inequality can be regarded as an optimization problem. In this paper we find another proof for a Chen's inequality,regarding the Ricci curvature [2] and we improve this inequality in the Lagrangian case.
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
Comparison of geometric quantities usually means obtaining generally true equalities of different algebraic expressions of a given geometric figure. Today's technical possibilities already support symbolic proofs of a conjectured theorem,…
In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].