26D15; 60E15.

In this paper, we generalize an open problem posed by Ngô et al. in [Notes
on an Integral Inequality, JIPAM, 7(4)(2006), Art. 120] and give some answers which extend the results of Boukerrioua-Guezane-Lakoud [On an open question regarding an integral inequality, JIPAM, 8(3) (2007), Art. 77.] and Liu-Li-Dong [On an open problem concerning an integral inequality, JIPAM, 8(3) (2007), Art. 74].