Some Properties Concerning the J_L(X) and Y_J(X) Which Related to Some Special Inscribed Triangles of Unit Ball

In this paper, we will make some further discussions on the $J_L\left(X\right)$ and $Y_J\left(X\right)$ which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants $L_1(X,▵)$, $L_2(X,▵)$ which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among $J_L\left(X\right)$, $Y_J\left(X\right)$ and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for $J_L\left(X\right)$, $Y_J\left(X\right)$ and some significant geometric constants, including the James constant $J\left(X\right)$ and the von Neumann-Jordan constant $C_{\mathrm{NJ}}\left(X\right)$. Finally, we introduce the two new geometric constants $L_1(X,▵)$, $L_2(X,▵)$, and calculate the bounds of $L_1(X,▵)$ and $L_2(X,▵)$ as well as the values of $L_1(X,▵)$ and $L_2(X,▵)$ for two Banach spaces.