Related papers: Chernoff's Inequality - A very elementary proof
In this short note, we improve the famous Reid Inequality related to linear operators.
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 improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
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…
A generalization of an inequality from IMO is proven.
In this note the Chernoff Theorem is used to approximate evolution semigroups constructed by the procedure of subordination. The considered semigroups are subordinate to some original, unknown explicitly but already approximated by the same…
We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.
In this note, we give a simple, counting based proof of Fisher's Inequality that does not use any tools from linear algebra.
In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We provide a very simple case showing that the weak form of the Heisenberg limit can be beaten while the prior information is improved without bias.
We study an inequality suggested by Littlewood, our result refines a result of Bennett.
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
In this short note, we give the refined Young inequality with Specht's ratio by only elementary and direct calculations. The obtained inequality is better than one previously shown by the author in 2012. In addition, we give a new property…
We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.