Related papers: A generalization of an inequality from IMO 2005

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

In this paper, we propose a generalization of a congruence due to Carlitz.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We give an alternative proof of a sharp generalization of an integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables, is possible. This last…

A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.

Following and generalizing unpublished work of Ange, we prove a generalized version of R\'emond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective…

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

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

We prove Burkholder inequality using Bregman divergence.

We establish an operator extension of the following generalization of Bohr's inequality, due to M.P. Vasi\'c and D.J. Ke\v{c}ki\'{c}: $$|\sum_{i=1}^n z_i|^r \leq (\sum_{i=1}^n \alpha_i^{1/(1-r)})^{r-1}\sum_{i=1}^n \alpha_i|z_i|^r \quad…

We study an inequality suggested by Littlewood, our result refines a result of Bennett.

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…

This note proves a version of Lubell-Yamamoto-Meshalkin inequality for general product measures.

An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).

We generalize the classical Minkowski integral inequality to the form involving general Banach function norms.

We improve constants in the Rademacher-Menchov inequality.

Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…

We present a generalization of a formula of higher order derivatives and give a short proof.