In this paper, we consider the max-product neural network operators of Kantorovich type based on certain linear combinations sigmoidal and ReLU activation functions. general, it is well-known that have applications in problems related to probability fuzzy theory, involving both real interval/set valued particular, here face inverse approximation for above family sub-linear operators. We first e...

The original transport problem is to optimally move a pile of soil to an excavation. Mathematically, given two measures of equal mass, we look for an optimal map that takes one measure to the other one and also minimizes a given cost functional. Kantorovich relaxed this problem by considering a measure whose marginals agree with given two measures instead of a bijection. This generalization lin...

An analogue of the quadratic Wasserstein (or Monge-Kantorovich) distance between Borel probability measures on $\mathbf{R}^d$ has been defined in [F. Golse, C. Mouhot, T. Paul: Commun. Math. Phys. 343 (2015), 165-205] for density operators $L^2(\mathbf{R}^d)$, and used to estimate convergence rate various asymptotic theories context quantum mechanics. The present work proves a Kantorovich type ...

Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

We consider a variational optimization problem involving multifunctions and we prove a stability result with respect to the Monge-Kantorovich metric. We then show an application to variational problems defined on fractals generated by Iterated Function Systems.

This is an overview of the life and scientific legacy of Leonid V. Kantorovich (1912--1986) who stood at the cradle of linear programming, vector lattices, and computational mathematics. Linear programming as well as mathematical economics belongs to or at least borders the realm of applied mathematics. The epithets “pure” and “applied” for mathematics have many deficiencies provoking endless d...

The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler’s inequality.

We apply the Poincaré inequality to study the extended Kantorovich method that was used to construct a closed-form solution for two coupled partial differential equations with mixed boundary conditions.

We consider the dispersive logarithmic Schr{\"o}dinger equation in a semi-classical scaling. extend results about large time behaviour of solution (dispersion faster than usual with an additional factor, convergence rescaled modulus to universal Gaussian profile) case constant. also provide sharp rate profile Kantorovich-Rubinstein metric through detailed analysis Fokker-Planck satisfied by thi...