Related papers: A Reverse Hilbert-like Optimal Inequality
We will formulate and prove a generalization of the isoperimetric inequality in the plane. Using this inequality we will construct an unitary space - and in consequence - an isomorphic copy of a separable infinite dimensional Hilbert space,…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
In this article we take a probabilistic look at H\"older's inequality, considering the ratio of terms in the classical H\"older inequality for random vectors in $\mathbb{R}^n$. We prove a central limit theorem for this ratio, which then…
Khabibullin's conjecture for integral inequalities has two numeric parameters $n$ and $\alpha$ in its statement, $n$ being a positive integer and $\alpha$ being a positive real number. This conjecture is already proved in the case where…
We shall give some results for an integer divisible by its unitary totient.
Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the…
We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…
We prove a sharp integral inequality valid for non-negative functions defined on $[0,1]$, with given $L^1$ norm. This is in fact a generalization of the well known integral Hardy inequality. We prove it as a consequence of the respective…
Let $A$ be a nonempty finite set of $k$ integers. Given a subset $B$ of $A$, the sum of all elements of $B$, denoted by $s(B)$, is called the subset sum of $B$. For a nonnegative integer $\alpha$ ($\leq k$), let \[\Sigma_{\alpha}…
The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…
In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…
In this note we find optimal one-sided majorants of exponential type for the signum function subject to certain monotonicity conditions. As an application, we use these special functions to obtain a simple Fourier analysis proof of the…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
We characterize approximate global optimal solutions (${\varepsilon}$-optima) to reverse optimization problems, namely, problems whose non-convex constraint is of the form $h(x) \geq 0$. This issue has not been addressed previously in the…
We consider the massive Thirring model in the laboratory coordinates and explain how the inverse scattering transform can be developed with the Riemann-Hilbert approach. The key ingredient of our method is to transform the corresponding…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…