Most important outcome of Iterated Function System is Collage Theorem. In this consequence, IFS is designed in D-metric space . Finally Collage theorem is established in D-metric space structure. Mathematics Subject Classification: 28A80, 54H25

In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil’s staircases) supported on limit sets of finitely generated conformal iterated function systems in R. For a large class of these Gibbs states we determine the Hausdorff dimension of the set of points at which the distribution function of these measures i...

Multiple iterated revision needs advanced belief revision techniques beyond the classical AGM theory that are able to integrate several (propositional) pieces of new information into epistemic states. A crucial feature of this kind of revision is that the multiple pieces of information should be dealt with separately, which has usually been understood as requiring some kind of independence amon...

We consider conditional random quantities (c.r.q.’s) in the setting of coherence. Given a numerical r.q. X and a non impossible event H, based on betting scheme we represent the c.r.q. X|H as the unconditional r.q. XH + μH, where μ is the prevision assessed for X|H. We develop some elements for an algebra of c.r.q.’s, by giving a condition under which two c.r.q.’s X|H and Y |K coincide. We show...

We study supports of M -re ̄nable functions by means of attractors of iterated function systems, where M is an integer greater than (or equal to) 2. Most of the time, the re ̄nable function Á is not explicitly known. We need to study their properties from the re ̄nement mask. Under the assumption of local linear independence, we show that the support equals to the attractor of an iterated function...

A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.

We prove that the family of all invariant sets of iterated systems of contractions R → R is a nowhere dense Fσ type subset in the space of the non-empty compact subsets of R equipped with the Hausdorff metric. An iterated function system (IFS for short) is a finite collection (T1, . . . , Tn) of weak contractions of a metric space X. By a weak contraction we mean a mapping T : X → X such that d...

in this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. in particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.

Boundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a po...