Results 41 to 50 of about 1,971,703 (365)

An operator inequality related to Jensen’s inequality [PDF]

Proceedings of the American Mathematical Society, 2001
Summary: For bounded non-negative operators \(A\) and \(B\), Furuta showed \[ 0\leq A \leq B \text{ implies } A^{\frac{r}{2}}B^sA^{\frac{r}{2}} \leq (A^{\frac{r}{2}}B^tA^{\frac{r}{2}})^{\frac{s+r}{t+r}}\quad (0\leq r, 0\leq s \leq t).
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On further refinements for Young inequalities

Open Mathematics, 2018
In this paper sharp results on operator Young’s inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young’s inequality.
Furuichi Shigeru, Moradi Hamid Reza
doaj   +1 more source

The Second-Order Differential Equation System with the Controlled Process for Variational Inequality with Constraints

Complexity, 2021
In this paper, the variational inequality with constraints can be viewed as an optimization problem. Using Lagrange function and projection operator, the equivalent operator equations for the variational inequality with constraints under the certain ...
Li Wang, Xingxu Chen, Juhe Sun
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New Refinement of the Operator Kantorovich Inequality

Mathematics, 2019
We focus on the improvement of operator Kantorovich type inequalities. Among the consequences, we improve the main result of the paper [H.R. Moradi, I.H. Gümüş, Z.
Hamid Reza Moradi, Shigeru Furuichi, Zahra Heydarbeygi   +2 more
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Operator Aczél inequality

Linear Algebra and its Applications, 2011
p pages; to appear in Linear Algebra Appl. (LAA)
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Around the Furuta inequality—the operator inequalities (AB2A)¾≤ABA≤A3

International Journal of Mathematics and Mathematical Sciences, 1995
For positive operators A and B with A invertible it is shown that (AB2A)½≤A2 implies (AB2A)¾≤ABA. The inequalities in the title for 0≤B≤A are then derived as a conquence.
Derming Wang
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New progress on the operator inequalities involving improved Young’s and its reverse inequalities relating to the Kantorovich constant

Journal of Inequalities and Applications, 2017
The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young’s and its reverse inequalities related to the Kittaneh-Manasrah inequality.
Jie Zhang, Junliang Wu
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An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds

, 2019
We prove \emph{optimal} improvements of the Hardy inequality on the hyperbolic space. Here, optimal means that the resulting operator is critical in the sense of [J.Funct.Anal. 266 (2014), pp.
Berchio, Elvise, Ganguly, Debdip, Grillo, Gabriele, Pinchover, Yehuda   +3 more
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Operator inequalities and normal operators

Banach Journal of Mathematical Analysis, 2012
Over the last years, a lot of work has appeared on operator inequalities. The present authors use some advantages offered by the context of finite-dimensional Hilbert spaces and establish complete characterizations of certain distinguished classes of operators (self-adjoint, unitary reflection, normal) in terms of operator inequalities.
Menkad, Safa, Seddik, Ameur
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Oscillatory and spectral properties of fourth-order differential operator and weighted differential inequality with boundary conditions

Boundary Value Problems, 2022
In the paper, we study the oscillatory and spectral properties of a fourth-order differential operator. These properties are established based on the validity of some weighted second-order differential inequality, where the inequality’s weights are the ...
Askar Baiarystanov, Aigerim Kalybay, Ryskul Oinarov   +2 more
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