Related papers: Chernoff's Inequality - A very elementary proof

We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski inequality of B\"or\"oczky, Lutwak, Yang and Zhang.

A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

The purpose of this note is to provide a detailed proof of Nazarov's inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017, Annals of Probability).

We give an elementary proof to Hasse theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

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 shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

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

The Chernoff bound is one of the most widely used tools in theoretical computer science. It's rare to find a randomized algorithm that doesn't employ a Chernoff bound in its analysis. The standard proofs of Chernoff bounds are beautiful but…

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .

We present an elementary proof for Ljunggren equation

In this note we prove a weighted version of the Khintchine inequalities.

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…

We present in this work a new and simple proof of the false centre theorem.

We obtain some inequalities which are stronger than the Schur majorization inequalities.

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

We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.