In this paper, we gave some generalized Young type inequalities due to Zuo and Li [J. Math. Inequal., 16 (2022), 1169-1178], and we also presented a new Young type inequality. As applications, we obtained some operator inequalities and matrix versions inequalities including the Hilbert-Schmidt norm and trace.

In this paper, we will give some AM-GM-HM singular values inequalities and some weighted power mean inequalities, our results generalized and complete the existed ones.