The functional Orlicz–Brunn–Minkowski inequality for q-torsional rigidity

In this paper, we obtain the functional Orlicz–Brunn–Minkowski inequality and the functional Orlicz–Minkowski inequality for q-torsional rigidity in the smooth category. Furthermore, using an approximation method, we give the general functional Orlicz–Brunn–Minkowski inequality for q-torsional rigidity. As a corollary, we reveal that the functional Orlicz–Brunn–Minkowski inequality is equivalent to the functional Orlicz–Minkowski inequality for q-torsional rigidity in the smooth category. We also give some applications with respect to these two inequalities.