In this short paper, we establish a reverse of the derived inequalities for sector matrices by Tan and Xie, with Kantorovich constant. Then, as application our main theorem, some determinant unitarily invariant norm are presented.

The famous Newton–Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton’s method to a solution of an equation. Here we present a “Kantorovich type” convergence analysis for the Gauss–Newton’s method which improves the result in [W.M. Häußler, A Kantorovich-type convergence analysis for the Gauss–Newton-method, Numer. Math. 48 (1986) 119–125...

In the operator version of the Hahn-Banach-Kantorovich theorem, the range space Y is assumed to be Dedekind complete. Y. A. Abramovich and A. W. Wickstead improved this by assuming only the Cantor property on Y . Along the same line of reasoning, we obtained in this paper several new results of this type. We also see that assuming Cantor property on the domain spaces instead gives good results,...

It is well-known that for Hilbert space linear operators 0 ≤ A and 0 ≤ C, inequality C ≤ A does not imply C ≤ A. We introduce a strong order relation 0 ≤ B≪ A, which guarantees that C ≤ BAB for all 0 ≤ C ≤ B, and that C ≤ A when B commutes with A. Connections of this approach with the arithmetic-geometric mean inequality of Bhatia–Kittaneh as well as the Kantorovich constant of A are mentioned.

We remind of the history of the transportation (Kantorovich) metric and the Monge–Kantorovich problem. We also describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one relates to Ornstein's theory of Bernoulli automorphisms (¯ d-metric), and the third one is the formulation of the ...

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials q > 0 attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∈ C : |z| < R}, R > q, the rate of approximation by the q-Kantorovich operators q > 1 is of order q−n versus 1/n for the classical K...

By looking at the Γ-convergence of some easy functionals in terms of underlying Young measures, we emphasize the connection of this issue with the Monge-Kantorovich mass transfer problem. After exploring this relationship, we study a typical example in periodic homogenization to realize the difference between the Monge-Kantorovich problem and the usual cell-problem. We also state a version of t...

2 Formulation of the mass transport problems 4 2.1 The original Monge-Kantorovich problem . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Guessing a good dual to the Monge-Kantorovich problem . . . . . . . . . . . . . 6 2.3 Properties of ”Extreme points of C” . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Existence of a minimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Abstract For sequences sufficiently close to ( a log n ), with an arbitrary real constant , this note describes the precise asymptotics of associated empirical distributions modulo one, respect Kantorovich metric as well discrepancy-style metric. In particular, demonstrates how these depend on in delicate, discontinuous way. The results strengthen and complement known facts literature.