  In this paper, we will improve and generalize inequality of Ostrowski type
for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . Some
well known inequalities can be derived as special cases. In addition, perturbed
mid-point inequality and perturbed trapezoid inequality are also obtained. The
obtained inequalities have immediate applications in numerical integration
where new estimates are obtained for the remainder term of the trapezoid and
midpoint formula. Applications to some special means are also investigated.
