Results 71 to 80 of about 7,376 (127)

Note on stability estimation of stochastic difference equations

Open Mathematics
Stability estimates are proposed for two variants of Markov processes defined by stochastic difference equations: uncontrolled and controlled. Processes of this type are widely used in applications where their “governing distributions” are known only ...
Gordienko Evgueni, Ruiz de Chavez Juan
doaj   +1 more source

Kantorovich type operator inequalities via the Specht ratio

Linear Algebra and its Applications, 2004
The generalized Specht ratio is defined for every \(r\in \mathbb{R}\), \(k> 0\), as \[ S_k(r)= {(k^r- 1)k^{{r\over k^r-1}}\over re\log k}\text{ when }k\neq 1\text{ and }S_1(r)= 1. \] This ratio has been used by some authors in the theory of Hilbert space operator inequalities. For example, \textit{J. I. Fujii}, \textit{T. Furuta}, \textit{T.
Fujii, Jun Ichi, Seo, Yuki, Tominaga, Masaru   +2 more
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Neural‐network‐based regularization methods for inverse problems in imaging

GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.
Abstract This review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for ...
Andreas Habring, Martin Holler
wiley   +1 more source

An extension of the operator Kantorovich inequality

Tbilisi Mathematical Journal, 2020
Let \(A\) be a positive invertible operator on a Hilbert space \(H\) such that \(mI\le A\le MI\) where \(I\) is the identity operator on \(H\) and \(m,M\) are positive real numbers. The celebrated Kantorovich inequality asserts that \[ \langle Ax,x\rangle \langle A^{-1}x,x\rangle \le \frac{(m+M)^2}{4mM} \] for all unit vectors \(x\in H\).
Khatib, Yaser, Hassani, Mahmoud, Amyari, Maryam   +2 more
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Mathematical analysis of a mesoscale model for multiphase membranes

GAMM-Mitteilungen, Volume 47, Issue 4, November 2024.
Abstract In this article, we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author (Arch. Ration. Mech. Anal. 193, 2009) for the one‐phase case.
Jakob Fuchs, Matthias Röger
wiley   +1 more source

Continuity of extensions of Lipschitz maps and of monotone maps

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract Let X$X$ be a subset of a Hilbert space. We prove that if v:X→Rm$v\colon X\rightarrow \mathbb {R}^m$ is such that v(x)−∑i=1mtiv(xi)⩽x−∑i=1mtixi$$\begin{equation*} {\left \Vert v(x)-\sum _{i=1}^m t_iv(x_i)\right \Vert} \leqslant {\left \Vert x-\sum _{i=1}^m t_ix_i\right \Vert} \end{equation*}$$for all x,x1,⋯,xm∈X$x,x_1,\dotsc,x_m\in X$ and all ...
Krzysztof J. Ciosmak
wiley   +1 more source

Enhanced Young-type inequalities utilizing Kantorovich approach for semidefinite matrices

Open Mathematics
This article introduces new Young-type inequalities, leveraging the Kantorovich constant, by refining the original inequality. In addition, we present a range of norm-based inequalities applicable to positive semidefinite matrices, such as the Hilbert ...
Bani-Ahmad Feras, Rashid Mohammad Hussein Mohammad   +1 more
doaj   +1 more source

An extension of Kantorovich inequality

, 2005
Let \(A\) be a (bounded linear) positive invertible operator acting on a Hilbert space \(H\) and let \(I=[m,M]\) be the convex hull of the spectrum of \(A\). The authors, as an extension of the Kantorovich inequality (KI): \((Ax,x)(A^{-1}x,x)\leq (m+M)^{2}/(4mM)\) (\(x\in H, \| x\| =1\)), propose the inequality (EKI): \((f(A)x,x)/g ((Ax,x)) \leq \max_ ...
IZUMINO, SAICHI, NAKAMURA, MASAHIRO
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Some new Young type inequalities

AIMS Mathematics
In this paper, we gave some generalized Young type inequalities due to Zuo and Li [J. Math. Inequal., 16 (2022), 1169-1178], and we also presented a new Young type inequality.
Yonghui Ren
doaj   +1 more source

A matrix version of Rennie’s generalization of Kantorovich’s inequality [PDF]

Proceedings of the American Mathematical Society, 1965
Let A be a positive definite hermetian matrix with eigenvalues l >X2 >_ * **X>n (A -XnI) (A -X11)A-1, where I is the unit matrix, is easily seen to be negative semi-definite since the first factor is positive semi-definite, the second negative semi-definite, the third positive definite and all three commute.
openaire   +1 more source