26D15,39B62,60E15.

By utilizing a reversed Hölder inequality and a reversed convolution inequality, some new integral inequalities which originate from an open problem posed in [F. Qi, Several integral inequalities, J. Inequal. Pure Appl. Math. 1(2) (2000), Art. 19. Available online at http://jipam.vu.edu.au/v1n2/001_00.html. RGMIA Res. Rep. Coll., 2(7) (1999), Art. 9, 1039-1042. Available online at http://rgmia.vu.edu.au/v2n7.html] are established.;