Davison in 2015 used the famous Banach Fixed Point Theorem to prove that a certain class of iterated function systems generated counterparts of the Hutchinson measure in the space of projection-valued measures. In this ...

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

The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods ...

In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family ...

In this note we obtain results regarding the preservation of homogeneity properties along the whole orbit of a given iterated function system (IFS). We have essentially two types of results. The first class of them contains ...

The classical self-similar fractals can be obtained as xed points of the iteration technique introduced by Hutchinson. The well known results of Mosco show that typically the limit fractal equipped with the invariant measure ...