An iterated function system consists of a complete metric space (X,d) and finite family contractions f1,⋯,fn:X→X. A generalized comprises defined on the Cartesian product Xm with values in X. In this paper, we want to investigate systems more general setting b-metric spaces. We prove that such admits unique attractor and, under some further restrictions b-metric, it depends continuously paramet...

Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure R does not equal its expected value, then underlying iterated function system contains an exact overlap. In recent years significant progress has been made towards these conjectures. Hochman proved that if Hausdorff there are cylinders which super-exponentially close at all...