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...

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.