Derivation and applications of inequalities of Ostrowski type for n-times differentiable mappings for cumulative distribution function and some quadrature rules

Abstract

In this paper new integral inequalities of Ostrowski type are developed for n-times differentiable mappings. Some well known inequalities become special cases of the inequalities obtained in this paper. With the help of obtained inequalities, we will derive new and efficient quadrature rules which are analyzed with the help of specific examples. We also give applications for cumulative distribution function.

Weighted Ostrowski's Type Integral Inequalities for Mapping Whose Second Derivative is Bounded

“…Then Cerone [2], Dragomir et al [3] and Sarıkaya et al [4] also worked on this inequality. A. Qayyum et al [5][6][7][8][9] worked on generalization of Ostrowski's type inequalities. Different authors worked on the generalization of Ostrowski's type inequalities that are [10], [11] and [12].…”