Results 31 to 40 of about 7,613 (204)

Extreme points of a ball about a measure with finite support [PDF]

, 2016
We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge-Wasserstein and Kantorovich metric balls about a measure whose support has at most n points, consist of ...
Owhadi, Houman, Scovel, Clint
core   +2 more sources

Multiple-Term Refinements of Young Type Inequalities

Journal of Mathematics, 2016
Recently, a multiple-term refinement of Young’s inequality has been proved. In this paper, we show its reverse refinement. Moreover, we will present multiple-term refinements of Young’s inequality involving Kantorovich constants.
Daeshik Choi
doaj   +1 more source

The Kantorovich Inequality under Integral Constraints

Journal of Mathematical Analysis and Applications, 1994
Let \(f: [0,1]\to [m,M]\), where \(0< m ...
MIGLIACCIO, LUCIA, L. Nania
openaire   +3 more sources

Optimal transportation, topology and uniqueness [PDF]

, 2010
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing the goods to be
Ahmad, Najma, Kim, Hwa Kil, McCann, Robert J.   +2 more
core   +4 more sources

Several Matrix Kantorovich-Type Inequalities

Journal of Mathematical Analysis and Applications, 1996
Let \(A\) and \(A_j\) be \(n \times n\) positive (semi-)definite Hermitian matrices with (nonzero) eigenvalues contained in the interval \([m,M]\), where \(0 < m < M\). Let \(V\) and \(V_j\) be \(n \times r\) matrices, \(B =\) block diag \((A_1, \dots, A_k)\), \(U^* = (V^*_1, \dots, V^*_k)\). Let \(R(A)\) denote the column space of \(A\).
Neudecker, H., Liu, S.
openaire   +2 more sources

Grüss-Type Bounds for the Covariance of Transformed Random Variables

Journal of Inequalities and Applications, 2010
A number of problems in Economics, Finance, Information Theory, Insurance, and generally in decision making under uncertainty rely on estimates of the covariance between (transformed) random variables, which can, for example, be losses, risks, incomes ...
Mart&#237;n Egozcue, Luis Fuentes Garc&#237;a, Wing-Keung Wong, Ri&#269;ardas Zitikis   +3 more
doaj   +2 more sources

Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

Mathematics
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 ...
Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu, Xueping Chen   +3 more
doaj   +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
openaire   +2 more sources

A glimpse into the differential topology and geometry of optimal transport

, 2012
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of ...
A. Figalli, A. Figalli, A. Figalli, A. Figalli, A. Figalli, A. Figalli, A. Pratelli, A. Pratelli, B. Pass, C. Smith, C. Villani, C. Villani, D. Cordero-Erausquin, F. Otto, F. Otto, F. R. Harvey, G. Alberti, G. G. Lorentz, G. J. Minty, G. Loeper, G. Loeper, G. Loeper, G. Monge, J. A. Mirrlees, J. Kitagawa, J. Li, J. Liu, J. Liu, J. Lott, J. Urbas, J.-C. Rochet, J.-D. Benamou, J.-P. Bourguignon, K. Hestir, K.-T. Sturm, L. A. Ambrosio, L. A. Caffarelli, L. A. Caffarelli, L. A. Caffarelli, L. Ambrosio, L. C. Evans, L. Forzani, L. Kantorovich, L. Rüschendorf, M. Feldman, M. J. P Cullen, M. Spence, M.-K. von Renesse, N. Ahmad, N. Ahmad, N. Gigli, N. S. Trudinger, N. S. Trudinger, P. Delanoë, P. Delanoë, P. Delanoë, P. W. Y. Lee, P. W. Y. Lee, P. W. Y. Lee, P.-A. Chiappori, R. J. McCann, R. J. McCann, R. J. McCann, R. J. McCann, R. J. McCann, R. J. McCann, R. J. McCann, R. M. Dudley, R. T. Rockafellar, Robert J. McCann, S. T. Rachev, T. C. Koopmans, T. Champion, V. L. Levin, W. Gangbo, W. Gangbo, W. Gangbo., W. Schachermayer, X.-J. Wang, X.-J. Wang, X.-N. Ma, Y. Brenier, Y. Brenier, Y. Yu, Y.-H. Kim, Y.-H. Kim, Y.-H. Kim   +86 more
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Approximations of Antieigenvalue and Antieigenvalue-Type Quantities

International Journal of Mathematics and Mathematical Sciences, 2012
We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type ...
Morteza Seddighin
doaj   +1 more source