Starting from q-Taylor formula for the functions of several variables and mean value theorems in q-calculus which we prove by ourselves, we develop a new methods for solving the systems of equations. We will prove its convergence and we will give an estimation of the error. 2004 Elsevier Inc. All rights reserved.

In contrast to its wealth of applications in mathematics, the Kantorovich metric started to be noticed in computer science only in recent years. We give a brief survey of its applications in probabilistic concurrency, image retrieval, data mining, and bioinformatics. This paper highlights the usefulness of the Kantorovich metric as a general mathematical tool for solving various kinds of proble...

In this paper we extend the contraction mapping method to prove various existence and uniqueness properties of (self-similar) random fractal measures, and establish exponential convergence results for approximating sequences defined by means of the scaling operator. For this purpose we introduce a version of the Monge Kantorovich metric on the class of probability distributions of random measur...

We construct a general type of multivortex solutions of the self-duality equations (the Bogomol'nyi equations) of (2+1) dimensional relativis-tic Chern-Simons model with the non-topological boundary condition near innnity. For such construction we use a modiied version of the Newton iteration method developed by Kantorovich.

A Newton-Kantorovich convergence theorem of a new modified Halley’s method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competence of our method. Finally, two numerical examples arising in the theory of the radiative transfer, neutron transport and in the kinetic theory of gasses are provided to show the applicatio...

The convergence properties of Newton’s method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale’s point estimate theorems as special cases, are obtained. Mathematics subject classification: 49M15, 65F20, 65H10.

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of ...

Abstract The main purpose of this paper is to use a power series summability method study some approximation properties Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya result.