G-convergence and G-sequential spaces

In this paper, for a method $G$ on a set $X$, we consider $G$-convergence and $G$-sequential convergence; we analyse the distinction between them with some counterexamples. Then, $G$-sequential continuity is investigated, and the relations between $G$-continuous and $G$-sequentially continuous functions are determined. Moreover, $G$-sequential spaces are introduced and studied. Finally, examples of $G$-sequential spaces associated with $G$-methods are given.