The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces

Let $\Phi$ be an $N$-function. Then the normal structure coefficients $N$ and the weakly convergent sequence coefficients $WCS$ of the Orlicz function spaces $L^\Phi[0,1]$ generated by $\Phi$ and equipped with the Luxemburg and Orlicz norms have the following exact values. (i) If $F_\Phi(t)=t\varphi(t)/\Phi(t)$ is decreasing and $1<C_\Phi<2$ (where $C_\Phi=\lim_{t\to+\infty}t\varphi(t)/\Phi(t)$), then
$$ N(L^{(\Phi)}[0,1])=N(L^{\Phi}[0,1])=WCS(L^{(\Phi)}[0,1])=WCS(L^{\Phi}[0,1])=2^{1-1/C_\Phi}. $$
(ii) If $F_\Phi(t)$ is increasing and $C_\Phi>2$, then
$$ N(L^{(\Phi)}[0,1])=N(L^{\Phi}[0,1])=WCS(L^{(\Phi)}[0,1])=WCS(L^{\Phi}[0,1])=2^{1/C_\Phi}. $$