Simpson’s Second Type Integral Inequalities for Twice Differentiable Convex Functions

Sabah Iftikhar, Ugochukwu David Uche

Abstract

In this paper, the authors used a new auxiliary integral identity involving twice differentiable function based on a three step quadratic kernel ω(s) and obtained several new integral inequalities of composite Simpson’s 3/8 type for functions whose second derivative absolute value power q are φ-convex and φ-quasiconvex function via Ho ̈lder’s and power mean inequality. Then we also obtain some Simpson’s second type integral inequalities as special cases of our main results and also provided some applications to special means.