Bellman–Steffensen type inequalities

Abstract

Abstract In this paper some Bellman–Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen’s inequality, nonnormalized versions of Steffensen’s inequality are obtained. Further, linear functionals, from obtained Bellman–Steffensen type inequalities, are produced and their action on families of exponentially convex functions is studied.

Keywords

• Steffensen’s inequality
• Bellman–Steffensen type inequality
• Measure theory
• Exponential convexity