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.
"Some perturbed trapezoid inequalities for convex, $s$-convex and $tgs$-convex functions and applications." Tbilisi Math. J. 8 (2) 87 - 102, December 2015. https://doi.org/10.1515/tmj-2015-0013