Superadditivity and monotonicity of some functionals associated with the Hermite-Hadamard inequality for convex functions in linear spaces

Abstract

The superadditivity and monotonicity properties of some func- tionals associated with convex functions and the Hermite-Hadamard inequality in the general setting of linear spaces are investigated. Applications for norms and convex functions of a real variable are given. Some inequalities for arithmetic, geometric, harmonic, logarithmic and identric means are improved.