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...

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...

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...

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...

In this paper we survey some notions of generalized derivative for C1,1 functions.Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

In this paper some second order necessary and sucient conditions aregiven for unconstrained and constrained optimization problems involving C1functions. A generalized derivative is obtained by approximation with smoothfunctions and it collapses to Clarke's definition when C(1,1) data are...

We present a two-sector endogenous growth model with human and physical capital accumulation in order to analyze the long run relationship between population growth and real per capita income growth. Learning is assumed to affect agents’ decision of how much to invest in formal education....

Using nonlinear optimization techniques in fractal image compression. Fractal image compression generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Most practical as well as theoretical works in image processing and...

Many definitions of second order generalized derivatives have been introduced to obtain optimality conditions for optimization problems involving C(1,1) data. The aim of this paper is to show some relations among these definitions and to study necessary and sufficient optimality conditions for...