Geodesic
On a Bessack's inequality related to Opial's and Hardy's
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 145

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Bessack [2] in 1979 used Holder's inequality to obtain an integral inequality which has as special cases Opial's and Hardy's. Here, using mainly Jensen's inequality for convex functions, with a non-negative, non-decreasing function in the operator, we obtain an integral inequality which is similar to Bessaack's but now containing a refinement term. When $l'(x)$ in Bessack [2] and $f$ in Imoru and Adeagbo-Sheikh [4] are restricted to being non-decreasing, these two inequalities become special cases of our results.
Classification : 47H06 47H10
Keywords: Opial's, Hardy's, Jensen's and Bessack's Inequalities and convex function 
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     author = {A. G. Adeagbo-Sheikh and O. O. Fabelurin},
     title = {On a {Bessack's} inequality related to {Opial's} and {Hardy's}},
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A. G. Adeagbo-Sheikh; O. O. Fabelurin. On a Bessack's inequality related to Opial's and Hardy's. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 145 . http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a11/