In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chao...

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

Let X be a compact metric space and f be a continuous map from X into itself. In this paper, we introduce the concept of the sequence asymptotic average shadowing property, which is a generalization of the asymptotic average shadowing property. In the sequel, we prove some properties of the sequence asymptotic average shadowing property and investigate the relationship between the sequence asym...