Some perturbed trapezoid inequalities for convex, $s$-convex and $tgs$-convex functions and applications

Abstract

In this paper, the Authors establish a new identity for twice differentiable functions. Afterwards some new inequalities are presented related to perturbed trapezoid inequality for the classes of functions whose second derivatives of absolute values are convex, $s$-convex and $tgs$-convex. Last of all, applications to special means have also been presented.