Some Inequalities for Differentiable Mappings and Applications to Fejér Inequality and Weighted Trapezoidal Formula

Abstract

In this paper, we establish some inequalities for differentiable convex mappings whose derivatives in absolute value are convex. This result is connected with Fejér’s inequality holding for convex mappings. Some applications for the weighted trapezoidal formula, $r−moment$, and the expectation of a symmetric and continuous random variable are given.