Geodesic
On a Bessack's inequality related to Opial's and Hardy's
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 145 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
@article{KJM_2011_35_1_a11,
     author = {A. G. Adeagbo-Sheikh and O. O. Fabelurin},
     title = {On a {Bessack's} inequality related to {Opial's} and {Hardy's}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {145 },
     year = {2011},
     volume = {35},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a11/}
}
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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/