Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301Some of the sufficient conditions to get the G-Bi-shadowing action11051112565210.22075/ijnaa.2022.5652ENMohammed Hussein ObaidAjamDepartment of Mathematics, Collage of Education for Pure Science, University of Babylon, Babylon, IraqIftichar Mudhar TalbAl-SharaaDepartment of Mathematics, Collage of Education for Pure Science, University of Babylon, Babylon, IraqJournal Article20210801The 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.https://ijnaa.semnan.ac.ir/article_5652_77bae5ef472b456103f5ea938586dd86.pdf