Related papers: An alternating proof of sharp inequalities related…
We consider the strong form of the John-Nirenberg inequality for the $L^2$-based BMO. We construct explicit Bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant as well as the precise…
We extend our previous work on sensitivity analysis for the risk ratio and difference contrasts under unmeasured confounding to any contrast. We prove that the bounds produced are still arbitrarily sharp, i.e. practically attainable. We…
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
We give an alternative proof of an elliptic summation formula of type $BC_n$ by applying the fundamental $BC_n$ invariants to the study of Jackson integrals associated with the summation formula.
In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.
This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…
We prove that the sharp constant in the univariate Bernstein--Nikolskii inequality for entire functions of exponential type is the limit of the sharp constant in the V. A. Markov type inequality with an exponential weight for coefficients…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
We prove that the previously established inequality of different metrics for algebraic polynomials is sharp in the sense of order.
We give a simple unified proof for several disparate bounds on Thurston-Bennequin number for Legendrian knots and self-linking number for transverse knots in R^3, and provide a template for possible future bounds. As an application, we give…
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-S\'andor means in terms of the arithmetic, harmonic, and contra-harmonic means…
We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's cube slicing inequality.
Plunnecke's inequality is the standard tool to obtain estimates on the cardinality of sumsets and has many applications in additive combinatorics. We present a new proof. The main novelty is that the proof is completed with no reference to…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
The sharp constants in the classical John--Nirenberg inequality are found by using Bellman function approach.