New proofs of Fejer's and discrete Hermite-Hadamard inequalities with applications

Abstract

New proofs of the classical Fejer inequality and discrete HermiteHadamard 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, ∞) → (0, ∞) is established