Related papers: Burkholder inequality by Bregman divergence

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

We prove an infinitary version of the Brauer-Schur theorem.

The Bregman divergence have been the subject of several studies. We do not go to do an exhaustive study of its subclasses, but propose a proof that shows that the \b{eta}-divergence are subclasses of the Bregman divergences. It is in this…

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…

The paper presents a counterexample to the Hodge conjecture.

We prove an inequality for the spectral norm of matrix valued stochastic integrals. This inequality can be seen either as a non-commutative version of the Burkholder-Davis-Gundy inequality or as an extension of the non-commutative…

We provide an alternating proof of sharp inequalities related with Burnside's formula for $n!$

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

We expose here a short proof of Cramer's theorem in R based on convex duality.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

We establish an inequality of different metrics for algebraic polynomials.

We provide a proof of the Borwein Conjecture using analytic methods.

A generalization of an inequality from IMO is proven.

We present a new proof of the Burkholder-Davis-Gundy inequalities for $1\leq p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a…

We obtain some new inequalities of Chebyshev Type.

We survey the classical results of the Dirichlet Approximation Theorem.

We prove a discrepancy estimate related to the sequence of fractional parts of $b^n/n$. This improves an earlier result of Cilleruelo et al.

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

A vector variational principle is proved.

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.