Topological version of generalized (infinite) iterated function systems

On the existence of the Hutchinson measure for generalized iterated function systems

“…As was proved by Matkowski [11], each Matkowski contraction satisfies the thesis of the Banach fixed point theorem (and this is one of the strongest generalization of the Banach theorem; for example, it implies the ones due to Browder, Rakotch or Edelstein-see [6] for a deep discussion on various contractive conditions). This assertion can be extended to the considered "generalized" case (see [4,Theorem 2.1] and also [13,16,23] for more restrictive cases).…”

“…The following result shows the promised relationships between a GIFS and its code space (see [ [4]). We just mention here the important, from the perspective of future reasonings, ones.…”

The Ergodic Theorem for a new kind of attractor of a GIFS

“…We will discuss that in the end of the Section 2.1. We should mention that recently, in 2015, Dumitru, Ioana, Sfetcu and Strobin [9] has considered many questions regarding to the extension of the concept of GIFS for topological contractions assuming that the family of maps is not just finite or countable but possibly an arbitrary family F of maps from X m to X, satisfying suitable hypothesis. Several results ar obtained by using code spaces (see [20] for details).…”

Fixed point theorems for nonlinear contractions with applications to iterated function systems

“…In recent years this area received great attention of many mathematicians, scientists and a huge developments took place (cf. [1,2,3,4,5,7,10,11,14,18,22,23,24,25,27,28,29,31,32,33]).…”