Search results for "Modes of convergence"

Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions

2016

[EN] We show a Dvoretzky-Rogers type theorem for the adapted version of the q-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector value…

Convergence in discrete Cauchy problems and applications to circle patterns

2005

A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.

Iterative approximation to a coincidence point of two mappings

2015

In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.

Boundary regularity and the uniform convergence of quasiconformal mappings

1979

On the Convergence of Formal Integrals in Finite Time

1982

Consider a differential system: x = f (x) + e g(x), \(x \in {R^n}.\). Let h(x) = ho(x) + eh1 (x)... a “third” integral. For finite time t, I obtain an eo such that the series h(x) converges if e > eo. When t tends to infinite, eo tends to zero.