Related papers: A Reverse Hilbert-like Optimal Inequality
We consider the inverse optimization problem associated with the polynomial program f^*=\min \{f(x): x\in K\}$ and a given current feasible solution $y\in K$. We provide a systematic numerical scheme to compute an inverse optimal solution.…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
The authors study statistical linear inverse problems in Hilbert spaces. Approximate solutions are sought within a class of linear one-parameter regularization schemes, and the parameter choice is crucial to control the root mean squared…
In this paper, we study the distribution of the digital reverses of prime numbers, which we call the "reversed primes". We prove the infinitude of reversed primes in any arithmetic progression satisfying straightforward necessary conditions…
In this paper, we give some reverse-types of Ando's and H\"older-McCarthy's inequalities for positive linear maps, and positive invertible operators. For our purpose, we use a recently improved Young inequality and its reverse.
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
We prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer $\ell\geq 1$, we improve the error term in the partial sums of the number of…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
A bilinear inequality of Geba, Greenleaf, Iosevich, Palsson, and Sawyer for the Fourier transform is shown to be equivalent to a simpler linear inequality, and the range of exponents is extended. Related mixed-norm inequalities are…
Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
This paper determines the sharp asymptotic order of the following reverse H\"older inequality for spherical harmonics $Y_n$ of degree $n$ on the unit sphere $\mathbb{S}^{d-1}$ of $\mathbb{R}^d$ as $n\to \infty$:…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…
A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces…
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*}…
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
In this note, we obtain a reverse version of the integral Hardy inequality on metric measure spaces. Moreover, we give necessary and sufficient conditions for the weighted reverse Hardy inequality to be true. The main tool in our proof is a…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.
The proof of the theorem concerning to the inverse cyclotomic Discrete Fourier Transform algorithm over finite field is provided.