Let B^p={z=(z_1,…,z_n)∈C^n| ‖z‖_p=<1}, where p is a real number not less than 1, be a Reinhardt domain in C^n and f(z)=(f_1(z), …, f_n(z)) be the normalized biholomorphic mapping in B^p, i.e, f(0) =0, J_f(0)=I, where J_f means the Jacobian of f, I means the identity matrix. In this note, we prove that: If f(z) is a nomalized biholomorphic convex mapping in B^p, p≥1, then is true, where ‖f(z)‖_p= As consequence, we have Actually, we can extend these results to the reinhardt domain D_p=, where p_1≥p_2≥…≥p_n≥1. We prove that: If f(z) is a nomalized biholomorphic convex mapping in D,,p_1≥p_2≥…≥p_n≥1, then is true, where ‖z‖~p= Moreover, we can extend (1) to the following inequality: where ‖f(z)‖_p=
