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Journal of Function Spaces
Volume 2016, Article ID 9324804, 6 pages
http://dx.doi.org/10.1155/2016/9324804
Research Article

Application of Functionals in Creating Inequalities

1Mechanical Engineering Faculty in Slavonski Brod, University of Osijek, Trg Ivane Brlić Mažuranić 2, 35000 Slavonski Brod, Croatia
2Department of Mathematics, Longyan University, Longyan, Fujian 364012, China

Received 14 July 2016; Accepted 27 September 2016

Academic Editor: Calogero Vetro

Copyright © 2016 Zlatko Pavić et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper deals with the fundamental inequalities for convex functions in the bounded closed interval. The main inequality includes convex functions and positive linear functionals extending and refining the functional form of Jensen’s inequality. This inequality implies the Jensen, Fejér, and, thus, Hermite-Hadamard inequality, as well as their refinements.