Some perturbed versions of the generalized trapezoid type inequalities for twice differentiable functions

Abstract

. In this study, we fi rst obtain an identity for twice differentiable functions. Then we es- tablish some new perturbed trapezoid type integral inequalities for functions whose fi rst derivatives either are of bounded variation or Lipschitzian. Moreover, some perturbed versions of trapezoid type inequalities for mapping whose second derivatives are bounded, of bounded variation or Lipschitzian, respectively.