Related papers: An equivalent form of Young's inequality with uppe…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
Improved model independent upper bounds on the weak transition form factors are derived using inclusive sum rules. Comparison of the new bounds with the old ones is made for the form factors h_{A_1} and h_V in B -> D* decays.
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 give a counterexample to a recently conjectured variant of the Penrose inequality.
The aim of this paper is to present some new Fejer-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.
In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
An unconditional inequality of the totient function is contributed to the literature. This result is associated with various problems about the distribution of prime numbers.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant $\delta$. The bound is expressed in the uniform entropy integral of…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.
In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…
The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
If $a,b$ are $n\times n$ matrices, Ando proved that Young's inequality is valid for their singular values: if $p>1$ and $1/p+1/q=1$, then $$ \lambda_k|ab^*|\le \lambda_k( \frac1p |a|^p+\frac 1q |b|^q ) \, \textit{ for all }k. $$ Later, this…
We improve the known upper bound for short exponential sums and increase the range on which a sharp upper bound is known.
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.
This paper presents some new inequalities, the most important of which is the inequality given in Theorem 2.1. It can solve a class of inequalities by a unified method. An important application of the inequality given in Theorem 2.1 is to…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…