One Concave-Convex Inequality and Its Consequences

Abstract

Our starting point is an integral inequality that involves convex, concave and monotonically increasing functions. We provide some interpretations of the inequality, in terms of both probability and terms of linear functionals, from which we further generate completely monotone functions and means. The latter application is seen from the perspective of monotonicity and convexity.

Keywords

• convex function
• completely monotone functions
• means
• random variable