We prove that any iterated function system of finite type possesses the weak separation property.

Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [8] proved that there exists a unique compact set K = K(I), called the attractor of the IFS I, such that K = ⋃m j=1 φj(K). Moreover, for any given probability vector p = (p1, . . . , pm), i.e. pj > 0 for all j and ∑m j=1 pj = 1, there exists a unique compactly supported proba...

In this work, we consider an impulsive non-autonomous semilinear equation with iterated deviating arguments in a Banach space. We establish the existence and uniqueness of a mild solution. Also we present an example that illustrates our main result.

This paper explores the generalization of fixed-point theorem for Fisher contraction on controlled metric space. The space and contractions are playing a very crucial role in this research. is used to generate new type fractal set called fractals (CF-Fractals) by constructing system named iterated function (CF-IFS). Furthermore, interesting results consequences demonstrated. In addition, collag...

In the framework of non-autonomous discrete dynamical systems in metric spaces, we propose new equilibrium points, called quasi-fixed and prove that they play a role similar to fixed points autonomous systems. this way some sufficient conditions for convergence iterative schemes type xk+1=Tkxk spaces are presented, where maps Tk contractivities with different points. The results include any reo...

We give a new approach to the study of conformal iterated function systems with arbitrary overlaps. We provide lower and upper estimates for the Hausdorff dimension of the limit sets of such systems; these are expressed in terms of the topological pressure and the function d, counting overlaps. In the case when the function d is constant, we get an exact formula for the Hausdorff dimension. We ...

We show that some results of the Hutchinson–Barnsley theory for finite iterated function systems can be carried over to the infinite case. Namely, if {Fi : i ∈ N} is a family of Matkowski’s contractions on a complete metric space (X, d) such that (Fix0)i∈N is bounded for some x0 ∈ X, then there exists a non-empty bounded and separable set K which is invariant with respect to this family, that i...