26D15

In the paper Several integral inequalitie published in J. Inequal. Pure Appl. Math., 1(2) (2000), Art. 19 and RGMIA Res, Rep. Coll., 2(7) (1999), Art. 9, 1039-1042, by F. Qi, an open problem was posed. In this article we give the solution and further generalizations of this problem without any differentiability of the integrands (although Qi's analytic approach). Reversed inequalities to the posed one are considered as well. Finally, the derived results are extended to the weighted integral inequalities.