Extensions of the Hermite-Hadamard inequality with applications
Copyright policy )Extensions of the Hermite-Hadamard inequality with applications
The main aim of this paper is to give improvements of various forms of the Hermite-Hadamard inequality, namely, that of Fejèr, Lupaş, Brenner-Alzer, Beesack-Pečarić. It is interesting that these improvements also imply the Hammer-Bullen inequality which deals with a comparison of the left-hand and the right-hand side of the Hermite-Hadamard inequality. These improvements are given in terms of positive linear functionals. Obtained results are used in constructing a new family of exponentially convex functions.
Hermite-Hadamard inequality, Fejér inequality, Hammer-Bullen inequality, Hermite-Hadamard inequality; Fejér inequality; Hammer-Bullen inequality; linear functionals, linear functionals
Hermite-Hadamard inequality, Fejér inequality, Hammer-Bullen inequality, Hermite-Hadamard inequality; Fejér inequality; Hammer-Bullen inequality; linear functionals, linear functionals
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