Related papers: A Bernstein type inequality

In our effort to find an arithmetically pure proof of the Bertrand postulate, we investigate and solve (using only elementary arithmetical methods) another less usual inequality in positive integers inspired by the classical proof of the…

We reduce the Nowicki conjecture on the Weitzenb\"ock derivation of polynomial algebras to well-known problem of the classical invariant theory.

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are…

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

We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.

In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.

We present inequalities and some applications to Kellers' limit and Carlemans' inequality.

We give a more strong heuristic justification of our conjecture on the excess of the odious primes.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…

We present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover,…

We prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.

We extend the inequality of Audenaert et al to general von Neumann algebras.

In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…

General considerations on the Equivalence conjectures and a review of few mathematical results.

This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.

We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…

In this paper, we consider a modified version of Smirnov operator and obtain some Bernstein-type inequalities preserved by this operator. In particular, we prove some compact generalizations of the well-known inequalities of Bernstein,…