Some of the sufficient conditions to get the G-Bi-shadowing action

Abstract

The aim of this paper is introduced some examples of a (mathbb{G})-bi-shadowing actions on the metric (mathbb{G})-space, by study a sufficient conditions of actions to be (mathbb{G})-bi-shadowing. We show the (mathbb{G})-(lambda)-Contraction actions, (mathbb{G})-(left( lambda,L right))textbf{-}Contraction action, and (mathbb{G})-Hardy-Rogers contraction action are (mathbb{G})-bi-shadowing by proved some theorems.