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 
@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 },
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a11/}
}
TY  - JOUR
AU  - A. G. Adeagbo-Sheikh
AU  - O. O. Fabelurin
TI  - On a Bessack's inequality related to Opial's and Hardy's
JO  - Kragujevac Journal of Mathematics
PY  - 2011
SP  - 145 
VL  - 35
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a11/
LA  - en
ID  - KJM_2011_35_1_a11
ER  - 
%0 Journal Article
%A A. G. Adeagbo-Sheikh
%A O. O. Fabelurin
%T On a Bessack's inequality related to Opial's and Hardy's
%J Kragujevac Journal of Mathematics
%D 2011
%P 145 
%V 35
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a11/
%G en
%F KJM_2011_35_1_a11
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/