Our main purpose of this article is to study the convergence and other related properties q-Bernstein-Kantorovich operators including shifted knots real positive numbers. We design Bernstein-Kantorovich generated by basic q-calculus. More precisely, we our new in space continuous functions Lebesgue space. obtain degree with help modulus continuity integral continuity. Furthermore, establish qua...

Double cnoidal waves of the Korteweg-de Vries equation are studied by direct solution of the nonlinear boundary value problem. These double cnoidal waves, which are the spatially periodic generalization of the well-known double soliton, are exact solutions with two independent phase speeds. The equation is written in terms of two phase variables and expanded in two-dimensional Fourier series. T...

The problem of optimal transportation between a set of sources and a set of wells has become recently the object of new mathematical models generalizing the Monge-Kantorovich problem. These models are more realistic as they predict the observed branching structure of communication networks. They also define new distances between measures. The question arises of how these distances compare to th...

In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, define Kantorovich extension of the operators. For functions belonging to space Lp [0, 1] , 1 ? p < ?, obtain convergence in norm by sequence Stancu-Kantorovich operators, and give an estimate for rate via first order averaged modulus smoothness. Moreover, operators; search variation detra...

The aim of this paper is to study the convergence and approximation properties of the bivariate operators and GBS operators of Kantorovich type.

The Newton–Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cos...

A probabilistic method for solving the Monge-Kantorovich mass transport problem on R is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle with an optimal transport cost as its rate function. As a consequence, new approximation results for the optimal cost function and the optimal transport plans ar...