The Kantorovich function (xT Ax)(xT A−1x), where A is a positive definite matrix, is not convex in general. From a matrix or convex analysis point of view, it is interesting to address the question: When is this function convex? In this paper, we prove that the 2dimensional Kantorovich function is convex if and only if the condition number of its matrix is less than or equal to 3 + 2 √ 2. Thus ...

In this paper, we apply four-dimensional infinite matrices to newly constructed original extension of bivariate Bernstein-Kantorovich type operators based on multiple shape parameters. We also use B?gel continuity construct the GBS (Generalized Boolean Sum) for defined Kantorovich type. Moreover, demonstrate certain illustrative graphs show applicability and validity proposed operators.

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 measures whose supports have at most n+2 points. Moreover, we use the Strassen and Kantorovich-Rubinstein duality theorems to develop representation...

Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as wel...

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 inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvaluetype qua...

We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without constraint qualification. As an example of application, the Monge-Kantorovich optimal transport problem is solved in great detail. In particular,...

The problem of finding all intersections between two surfaces has many applications in computational geometry and computer-aided geometric design. We propose an algorithm based on Newton’s method and subdivision for this problem. Our algorithm uses a test based on the Kantorovich theorem to prevent the divergence or slow convergence problems normally associated with using unsuitable starting po...

This paper is dedicated to the problem of isolating and validating zeros non-linear two point boundary value problems. We present a method for such purpose based on Newton-Kantorovich Theorem rigorously enclose isolated with Neumann conditions.