Improved Results of Perturbed Inequalities for Higher-Order Differentiable Functions and their Various Applications

Abstract

A new integral equality for the function whose higher order derivatives are absolutely continuous are first improved by using the quadratic kernel mapping with five sections. After that, refined inequalities of perturbed Ostrowski type for bounded functions and mappings of bounded variation are developed. What's more, new effective composite quadrature rules are derived to find closer estimates of the integral of a mapping. Some applications for exponential and logarithmic functions are also obtained by using inequalities presented in this study. Finally, new results involving Cumulative Distribution, the reliability function and expectation value of random variable are given.