on periodic shadowing property

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 chaotic in the sense of li-yorke. moreover, any distal homeomorphisms on a compact metric space with the periodic shadowing property do not have the asymptotic average shadowing property.