Improved version of perturbed Ostrowski type inequalities for n -times differentiable mappings with three-step kernel and its application

New integral inequalities of Ostrowski type are developed for n-times differentiable mappings by using a 3-step kernel when either f ( n ) ∈ L 1 [ a ; b ] or f ∈ L 2 [ a ; b ] . Some new inequalities are derived as special cases of the obtained inequalities. New efficient quadrature rules are also derived with the help of obtained inequalities. The efficiency of the new quadrature rules is demonstrated with the help of specific examples. Finally, applications for cumulative distribution functions is also provided.