A simple procedure to map two probability measures in R is the so-called Knothe-Rosenblatt rearrangement, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the...

In this paper, a new analogue of Bernstein-Kantorovich operators as (p, q)-Bernstein-Kantorovich operators are introduced. We discuss approximation properties for these operators based on Korovkin’s type approximation theorem and we compute the order of convergence using usual modulus of continuity and also the rate of convergence when the function f belongs to the class LipM (α). Moreover, the...

The paper establishes that a generalization of Monge–Kantorovich equation gives rise to necessary and sufficient optimality condition for the Kantorovich dual problem minimal flow associated with very degenerate Finsler metric without any assumption on coerciveness.

We establish necessary and sufficient conditions of solvability the nonlinear boundary-value problem in critical case. By using Newton–Kantorovich method, we propose a new iterative scheme for construction solutions weakly system ordinary differential equations

This is an expository talk on interaction between mathematical programming and vector lattices at the Kantorovich Memorial (St. Petersburg, January