Stancu type operators play a crucial role in convergence estimates. The present article concerns the estimates for certain Kantorovich operators. We first establish some direct formulas giving local approximation theorem, Voronovskaja asymptotic formula, bound second central moment with curtailment, and global theorem by means of modulus continuity Ditzian-Totik Modulus smoothness. also study d...

The multistochastic Monge–Kantorovich problem on the product X = ? i 1 n of spaces is a generalization multimarginal problem. For given integer number ? k < we consider minimization ? c d ? ? inf space measures with fixed projections onto every × … for arbitrary set indices { , } ? . In this paper study basic properties problem, including well-posedness, existence dual solution, boundedness and...

We prove that c-cyclically monotone transport plans π optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani’s book. We emphasize that we do not need any regularity condi...

We define a monad on the category of complete metric spaces with short maps, which assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich–Wasserstein distance. It is analogous to the Giry monad on the category of Polish spaces, and it extends a construction due to van Breugel for compact and for 1bounded complete metric spaces...

Newton’s method and its variants are among the most efficient methods known for solving systems of non-linear equations when the functions involved are continuously differentiable. Besides its practical applications, Newton’s method is also a powerful theoretical tool. Therefore, it has been studied and used extensively. One of the famous results on Newton’s method is the well-known Kantorovich...

Let 1; ; N be Borel, probability measures on R

In this paper, Lupa? Bernstein-Kantorovich operators have been studied using Jackson and Riemann type (p,q)-integrals. It has shown that (p, q)-integrals as well are not defined for 0 &lt; q p 1 thus further analysis is needed. Throughout the case ? used. Advantages of discussed over general q)-integrals. constructed via integral need be positive every f 0. So to make these based on q)-integral...

Boundary value problems posed over thin solids are often amenable to a dimensional reduction in that one or more spatial dimensions may be eliminated from the governing equation. One of the popular methods of achieving dimensional reduction is the Kantorovich method, where based on certain a priori assumptions, a lower-dimensional problem over a ‘mid-element’ is obtained. Unfortunately, the mid...