New Proofs of Fejer's and Discrete Hermite-Hadamard Inequalities With Applications

Abstract

New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions f : [a, b] -> R about the midpoint c = (a+b)/2 are obtained and the reverse Hardy inequality for convex functions f : (0, infinity) -> (0, infinity) is established.