Some Inequalities for N-Times Differentiable s-Convex and tgs-Convex Functions

Abstract

The aim of this study is to present some inequalities for n-times differentiable functions. These inequalities are associated with the perturbed trapezoid inequality. n th derivatives of absolute values of the considered functions are s-convex and tgs-convex. In previous studies, some inequalities for the classes of twice differentiable functions which are convex, s-convex and tgs-convex have been introduced. We expand twice differentiable functions to n-times differentiable functions. Finally, some applications are given to verify new inequalities proposed in this study.