Given an Ap-Muckenhoupt weight on a fractal obtained as the attractor of iterated function system, we construct sequence approximating weights, which are simple functions belonging uniformly to Ap class spaces.

k=0 (−1)k 2k + 1 x } , the sequence of Taylor polynomials centered at 0 that converges to arctanx on [−1, 1]. Like the Taylor polynomials for several other classical functions, e.g., cosx, sinx, and ex, this sequence of polynomials is very easy to describe and work with; but unlike those Taylor sequences with factorials in the denominators of their coefficients, it does not converge rapidly for...

Ill posed problems constitute the mathematical model of a large variety of applications. Aim of this paper is to define an iterative algorithm finding the solution of a regularization problem. The method minimizes a function constituted by a least squares term and a generally nonlinear regularization term, weighted by a regularization parameter. The proposed method computes a sequence of iterat...

Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing. In this way the approximating solution is coupled to the reference solution at a discrete sequ...

We consider approximations of a smooth convex body by inscribed and circumscribed convex polytopes as the number of vertices, resp. facets tends to innnity. The measure of deviation used is the diierence of the mean width of the convex body and the approximating polytopes. The following results are obtained. (i) An asymptotic formula for best approximation. (ii) Upper and lower estimates for st...

We establish the density of partial regularity result in class continuous viscosity solutions. Given a fully nonlinear equation, we prove existence sequence entitled to result, approximating its Distinct conditions on operator driving equation lead different topologies. Our findings include applications inhomogeneous problems, with variable-coefficients models.

We develop a unifying approach for approximating a “limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or “almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

We develop a unifying approach for approximating a \limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or \almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...