相关论文: A new proof of the AM-GM-HM inequality

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

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 note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.

A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights

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.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

Aim of this article is to prove the inequality $n \sum_{i=1}^{n} a_ib_i \leq \sum_{i=1}^{n} a_i \sum_{i=1}^n b_i$ when $a_i$ are $n$ increasing positive real numbers and $b_i$ are $n$ decreasing real numbers. We also prove generalizations…

The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…

The purpose of the paper is to present an short proof of the Chuang's inequality.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

We obtain simple proofs of certain inequalites for bivariate means.

In this note we prove an inequality involving primes and the product of consecutive primes.

We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

We give a very short proof of the Golden-Thompson inequality