Related papers: Variations on an inequality from IMO'2001
A generalization of an inequality from IMO is proven.
Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other…
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
A rule to assign a physical meaning to Lagrange multipliers is discussed. Examples from mechanics, statistical mechanics and quantum mechanics are given.
Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
We prove some extensions of Andrews inequality.
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 study the Lagarias inequality, an elementary criterion equivalent to the Riemann Hypothesis. Using a continuous extension of the harmonic numbers, we show that the sequence $B_n=\frac{H_n+e^{H_n}\log(H_n)}{n}$ is strictly increasing for…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
In the seminal book M\'echanique analitique, Lagrange, 1788, the notion of a Lagrange multiplier was first introduced in order to study a smooth minimization problem subject to equality constraints. The idea is that, under some regularity…
We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.
An improvement of a global Gagliardo-Nienberg inequality with a BMO term is established.
We prove existence and uniqueness of solution of an evolutionary vector-valued variational inequality defined in the convex set of vector valued functions $\boldsymbol v$ subject to the constraint $|\boldsymbol v|\le1$. We show that we can…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.
An improvement of a {\em Global (strong) Gagliardo-Nienberg inequality with a BMO term} is established by replacing local derivatives by {\em and fractional Laplacians.} Local versions are also given.
We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…