Generalization of Popoviciu type inequalities for symmetric means generated by convex functions
Abstract
In this paper an inequality of Popoviciu, which was improved by Vasic and Stankovic [13], is generalized by using Green function. An extension of Popoviciu type inequality is introduced. The mean value theorems, nexponential convexity and exponential convexity are presented for the differences of these inequalities and related Cauchy means are also generated.
Copyright © 2014 Josip Pecaric, Khuram Ali Khan, Ivan Peric. 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.
Cite this article
J. Pecaric, K. A. Khan, I. Peric, Generalization of Popoviciu type inequalities for symmetric means generated by convex functions, J. Math. Comput. Sci. 4 (2014), 1091–1113.
BibTeX
@article{Pecaric2014,
author = {Pecaric, Josip and Khan, Khuram Ali and Peric, Ivan},
title = {Generalization of Popoviciu type inequalities for symmetric means generated by convex functions},
journal = {J. Math. Comput. Sci.},
volume = {4},
year = {2014},
pages = {1091--1113},
doi = {}
}