A convergence theorem with boundary

Pointwise Convergence on the Boundary in the Denjoy-wolff Theorem

If φ is an analytic selfmap of the disk (not an elliptic automorphism) the DenjoyWolff Theorem predicts the existence of a point p with |p| ≤ 1 such that the iterates φn converge to p uniformly on compact subsets of the disk. Since these iterates are bounded analytic functions, there is a subset of the unit circle of full linear measure where they are all well-defined. We address the question o...

A stochastic approximation scheme and convergence theorem for particle interactions with perfectly reflecting boundary conditions

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and drift of the set of particles. Each particle carries a number of internal coordinates which may evolve continuously in time, determined by what we will refer to ...

A metastable dominated convergence theorem

The dominated convergence theorem implies that if (fn) is a sequence of functions on a probability space taking values in the interval [0, 1], and (fn) converges pointwise a.e., then ( ∫ fn) converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound...

A Convergence Theorem For Controlled . . .

A convergence theorem on the iterative solution of nonlinear two-point boundary-value systems

The nonlinear two-point boundary value problem occurs quite naturally in studies in many diverse science branches. For obtaining the approaching solution of the nonlinear problem we often replace the nonlinear problem with a sequence of linear problems in such a manner that the sequence of solutions to the linear problems approach in a limiting sense the solution of the nonlinear problem. The c...