We establish the inequality [equation] where α = CK,n = p/q,q − 1 + (u′(x)R(x)/u2(x)r(x)) ≥ q/K and R(x) = ∫x0r(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).
Journal of Mathematical Analysis and Applications 233(1), pp.193-204