Firstly, it is introduced that the concepts of G-almost periodic point and G-sequence shadowing property. Then, we discuss dynamical relationship between sequence map {gk}∞k=1 limit g under G-strongly uniform convergence topological group action. We can get (1) Let be converge to where equicontinuous {yk}∞k=1 {gk}∞k=1. If limk → ∞ yk = y, then y an g; (2) are equicontinuous, limsup APG(gk) ⊂ AP...