Related papers: A generalization of an inequality from IMO 2005
Motivated by previous work leveraging factorizations of second- and fourth-order differential operators, a general integral inequality involving higher order derivatives is proven by elementary means. It is then shown how this framework…
This paper states and proves a generalization of the well-known Desargues involution theorem from plane projective geometry.
An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.
In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…
In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…
We prove some symmetric $q$-congruences.
We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.
The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.
We provide a proof of the sharp log-Sobolev inequality on a compact interval.
We extend Dragomir's refinement of Jensen's inequality from the dicrete to the general case, identifying the equality conditions.
Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \langle\mathbf{v}^2,\mathbf{w}^2\rangle \leq…
In this note we show that McGee's {\omega}-inconsistency result can be derived from L\"ob's theorem.
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
We prove several generalisations of the ping-pong lemma for negatively curved groups.
We generalize an inequality conjectured by Pohst in 1977 and recently proved by the author and independently by Battistoni and Molteni. This new inequality improves a bound for the regulator in terms of the discriminant for totally real…
We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.