Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (6)

Search Parameters:
Keywords = kantorovich inequality

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
13 pages, 259 KiB  
Article
Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics
by Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu and Xueping Chen
Mathematics 2024, 12(18), 2860; https://doi.org/10.3390/math12182860 - 14 Sep 2024
Cited by 1 | Viewed by 679
Abstract
By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard [...] Read more.
By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models. Full article
(This article belongs to the Special Issue New Advances in High-Dimensional and Non-asymptotic Statistics)
15 pages, 301 KiB  
Article
Generalized Choi–Davis–Jensen’s Operator Inequalities and Their Applications
by Shih Yu Chang and Yimin Wei
Symmetry 2024, 16(9), 1176; https://doi.org/10.3390/sym16091176 - 9 Sep 2024
Cited by 1 | Viewed by 1324
Abstract
The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize [...] Read more.
The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics. Full article
(This article belongs to the Special Issue Research on Structured Matrices and Applications)
10 pages, 335 KiB  
Article
A New Kantorovich-Type Rational Operator and Inequalities for Its Approximation
by Esma Yıldız Özkan
Mathematics 2022, 10(12), 1982; https://doi.org/10.3390/math10121982 - 8 Jun 2022
Cited by 3 | Viewed by 1525
Abstract
We introduce a new Kantorovich-type rational operator. We investigate inequalities estimating its rates of convergence in view of the modulus of continuity and the Lipschitz-type functions. Moreover, we present graphical comparisons exemplifying concretely its better approximation for a certain function. The results of [...] Read more.
We introduce a new Kantorovich-type rational operator. We investigate inequalities estimating its rates of convergence in view of the modulus of continuity and the Lipschitz-type functions. Moreover, we present graphical comparisons exemplifying concretely its better approximation for a certain function. The results of the paper are crucial by means of possessing at least better approximation results than an existing Kantorovich-type rational function. Full article
(This article belongs to the Special Issue Mathematical Inequalities with Applications)
►▼ Show Figures

Figure 1

21 pages, 375 KiB  
Article
A Generalized Equilibrium Transform with Application to Error Bounds in the Rényi Theorem with No Support Constraints
by Irina Shevtsova and Mikhail Tselishchev
Mathematics 2020, 8(4), 577; https://doi.org/10.3390/math8040577 - 13 Apr 2020
Cited by 8 | Viewed by 2939
Abstract
We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties. In particular, we prove an optimal moment-type inequality for the Kantorovich distance between a distribution and its equilibrium transform. [...] Read more.
We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties. In particular, we prove an optimal moment-type inequality for the Kantorovich distance between a distribution and its equilibrium transform. Using the introduced transform and Stein’s method, we investigate the rate of convergence in the Rényi theorem for the distributions of geometric sums of independent random variables with identical nonzero means and finite second moments without any constraints on their supports. We derive an upper bound for the Kantorovich distance between the normalized geometric random sum and the exponential distribution which has exact order of smallness as the expectation of the geometric number of summands tends to infinity. Moreover, we introduce the so-called asymptotically best constant and present its lower bound yielding the one for the Kantorovich distance under consideration. As a concluding remark, we provide an extension of the obtained estimates of the accuracy of the exponential approximation to non-geometric random sums of independent random variables with non-identical nonzero means. Full article
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
6 pages, 209 KiB  
Article
On Improvements of Kantorovich Type Inequalities
by Chang-Jian Zhao and Wing-Sum Cheung
Mathematics 2019, 7(3), 259; https://doi.org/10.3390/math7030259 - 13 Mar 2019
Cited by 1 | Viewed by 2084
Abstract
In the paper, we give some new improvements of the Kantorovich type inequalities by using Popoviciu’s, Hölder’s, Bellman’s and Minkowski’s inequalities. These results in special case yield Hao’s, reverse Cauchy’s and Minkowski’s inequalities. Full article
7 pages, 223 KiB  
Article
New Refinement of the Operator Kantorovich Inequality
by Hamid Reza Moradi, Shigeru Furuichi and Zahra Heydarbeygi
Mathematics 2019, 7(2), 139; https://doi.org/10.3390/math7020139 - 1 Feb 2019
Viewed by 2886
Abstract
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. Heydarbeygi, A glimpse at the operator Kantorovich inequality, Linear Multilinear Algebra, doi:10.1080/03081087.2018.1441799]. Full article
(This article belongs to the Special Issue Inequalities)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop