The property of inverse shadowing in G-group with general properties of sequences

The property of inverse shadowing is studied in ℤ- group with the following properties: structurally stable, transversality property, Anosov, expansivity, continuum–wise expansive and expanding. Besides, this property is defined in G- group and studies general properties and relations like transitivity and sensitivity which are the most two important chaotic properties. In order for this property and sequences to be related as in ℤ- group and the property of shadowing, we define this property of G-inverse shadowing as a sequence of mappings on compact metric G-space and study this property in uniformly conjugate with the product.