In the operator version of the Hahn-Banach-Kantorovich theorem, the range space Y is assumed to be Dedekind complete. Y. A. Abramovich and A. W. Wickstead improved this by assuming only the Cantor property on Y . Along the same line of reasoning, we obtained in this paper several new results of this type. We also see that assuming Cantor property on the domain spaces instead gives good results,...

This paper proposes a parallel solver for the nonlinear systems in Bernstein form based on subdivision and the Newton-Raphson method, where the Kantorovich theorem is employed to identify the existence of a unique root and guarantee convergence of the Newton-Raphson iterations. Since the Kantorovich theorem accommodates a singular Jacobian at the root, the proposed algorithm performs well in a ...

We remind of the history of the transportation (Kantorovich) metric and the Monge–Kantorovich problem. We also describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one relates to Ornstein's theory of Bernoulli automorphisms (¯ d-metric), and the third one is the formulation of the ...

The extended principle of minimal action is described in the presence of prescribed source and sink points. Under the assumption of zero net flux, it leads to an optimal Monge-Kantorovich transport problem of metric type. We concentrate on action corresponding to a mecahnical Lagrangian. The optimal solution turns out to be a measure supprted on a graph composed of geodesic arcs connecting pair...

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials q > 0 attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∈ C : |z| < R}, R > q, the rate of approximation by the q-Kantorovich operators q > 1 is of order q−n versus 1/n for the classical K...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

Given a sequence {xn}n=Q in a Banach space, it is well known that if there a sequence {r^J^—QSUch that Wxn+X — xn\\ < tn + x — tn and lim tn = t* < °°, then {xn}n=Q converges to some x* and the error bounds IIjc* — jc II < f* — tn hold. It is shown that certain stronger hypotheses imply sharper error bounds, ■**-*„« <—-—Jxn-Xn-X*11* * \'*1-'0|M" > »• Representative applications to infinite seri...