Some properties of G – inverse shadowing property

Abstract

An actions Φ on compact metric G – space M are shown to have G – inverse shadowing property with respect to a class of d – methods which are represented by continuous mappings. We proved that fgg_j has G – inverse shadowing property if f_g has this property and the converse also true for all j ∈ ℕ. And f_g ο h_g, f_g × k_g, f_g + h_g, f_g − h_g, and f_g·h_g also have G – inverse shadowing property if f_g and h_g have G – inverse shadowing property. Finally, we showed that this property is deserved in the topologically conjugate with respect to the classes of homeomorphisms methods : if there exists a homeomorphism h_g on M such that f_g ο h_g = h_g ο k_g then f_g has G – inverse shadowing property with respect to the classes of homeomorphism methods if k_g has G – inverse shadowing property with respect to the classes of homeomorphism methods.