On an Open Problem of F. Qi

Volume 3, Issue 4, 2002

Article 54

ON AN OPEN PROBLEM OF F. QI

DEPARTMENT OF SCIENCES,
FACULTY OF MARITIME STUDIES,
UNIVERSITY OF RIJEKA,
51000 RIJEKA, STUDENTSKA 2,
CROATIA.
E-Mail: poganj@brod.pfri.hr

Received 16 November, 2001; Accepted 21 February, 2002.
Communicated by: N. Elezovic

ABSTRACT. 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.

Key words:
Integral inequality, Integral Hölder inequality, Reverse Hölder inequality, Nehari inequality, Barnes-Godunova-Levin inequality, Weighted integral inequality, Pecaric inequality.

2000 Mathematics Subject Classification:
26D15.

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