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

Document Type : Research Paper

Authors

Department of Mathematics, Collage of Education for Pure Science, University of Babylon, Babylon, Iraq

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.

Keywords