Submultiplicative and Power Submultiplicative Properties for Generalized Hersch-Pfluger Distortion Function

For $a\in(0,1/2]$ and $r\in(0,1)$, and for $K>0$, we investigate submultiplicative and power submultiplicative properties for generalized Hersch-Pfluger distortion function $\varphi_K^a(r)$, which generalize the recent results of Hersch-Pfluger distortion function $\varphi_K(r)$ obtained by Wang, Qiu and Chu.