Abstract This paper extends public spending-based growth theory along three directions: we assume that exogenous and constant technological progress does exist and that both population change and the ratio of government expenditure to income follow a logistic trajectory. By focusing on the...

We study the properties of multifunction operators that are contractive in the Covier-Nadler sense. In this situation, such operators $T$ possess fixed points satisying the relation $x \in Tx$. We introduce an iterative method involving projections that guarantees convergence from any starting...

Most natural phenomena or the experiments that explore them are subject to small variations in the environment within which they take place. As a result, data gathered from many runs of the same experiment may well show differences that are most suitably accounted for by a model that...

Many inverse problems in applied mathematics can be formulated as the approximation of a target element $u$ in a complete metric space $(X,d)$ by the fixed point $\bar x$ of an appropriate contraction mapping $T : X \to X$. The method of {\em collage coding} seeks to solve this problem by...

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L^2 decomposition like the...

Fractal image coding generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Generally, images are represented as functions u(x) and the fractal coding method is conducted in the framework of L2 or L1. Here we formulate a method...

In this paper, we develop a general collage coding framework for inverse problems in partial differential equations (PDEs) with boundary conditions. Although a general PDEs inverse problem can be very complicated, via the Generalized Collage Theorem in this paper, many such problems can be...

We introduce a method of iterated function systems (IFS) over the space of set-valued mappings (multifunctions). This is done by first considering a couple of useful metrics over the space of multifunctions F(X,Y). Some appropriate IFS-type fractal transform operators T:F(X,Y)-F(X,Y) are then...

In this paper, we study some IFS Markov operators on set-valued measures (multimeasures). For this, we consider countable additivity with respect to the Minkowski sum of compact and convex sets and countable additivity with respect to (the Hausdorff closure of) unions of compact sets. After...

In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations $T(w,x(w))=x(w)$ where $T:\Omega\times X\to X$ is a given operator, $\Omega$ is a probability space and $X$ is a complete metric space. The inverse problem is solved by...