Generalizations of Some Reverse Integral Inequalities

We establish the inequality 1rp 1rq 1 a p 1 a q Hr x.f x. dx/ Hr x.f x. dx/ R a.0 R a.0 a nq1 1rp F , a yn a y1. where a sCK, nsprq, qy1q u9 x.R x.ru2 x.r x..GqrK and R x.s H0xr t.u t. dt, which is sharper than that obtained by B. Mond, J. Pecaric, and I. Peric J. Math. Anal. Appl. 203 1996., 381]387..