About G-convergence and G-sequentially convergence

In this paper we will discuss the similarities and differences for some topological properties in $G$-continuity and $G$-sequential continuity. In particular we will illustrate the ways in which these notions agree and are divided in some topological properties by looking at their definitions, characteristics, and implications. We will use examples from the literature \cite{counterexample} to distinguish between G-continuity and G-sequential continuity. Moreover, we will prove that these two kinds of continuity produce different outcomes and broaden the notion of the G-method in topological spaces.