Proper resolutions and Gorensteinness in extriangulated categories

Let ( $$\mathscr{C},\mathbb{E},\frak{s}$$ ) be an extriangulated category with a proper class ? of $$\mathbb{E}$$ -triangles, and $$\mathscr{W}$$ additive full subcategory ). We provide method for constructing (?)-resolution (resp., coproper (?)-coresolution) one term in -triangle from that the other two terms. By using this way, we establish stability Gorenstein $$\mathscr{G}\mathscr{W}$$ (?) categories. These results generalize work Z. Y. Huang [J. Algebra, 2013, 393: 142–169] X. Yang C. Wang [Rocky Mountain J. Math., 2017, 47: 1013–1053], but proof is not too far their case. Finally, give some applications about our main results.