Generalized Steffensen Type Inequalities Involving Convex Functions

Abstract

In this paper generalized Steffensen type inequalities related to the class of functions that are “convex at point c” are derived and as a consequence inequalities involving the class of convex functions are obtained. Moreover, linear functionals from the difference of the right- and left-hand side of the obtained generalized inequalities are constructed and new families of exponentially convex functions related to constructed functionals are derived.