Generalization of Popoviciu type inequalities via Green function and Abel-Gontscharoff interpolating polynomial
Abstract
The inequality of Popoviciu for convex functions is generalized via Abel-Gontscharoff interpolating polynomial for higher order convex functions. Bounds are found for new identities, exponential convexity and Cauchy means are presented for linear functionals coming from the general inequality.
Copyright © 2017 Saad Ihsan Butt, Khuram Ali Khan, Josip Pecaric. 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
S. I. Butt, K. A. Khan, J. Pecaric, Generalization of Popoviciu type inequalities via Green function and Abel-Gontscharoff interpolating polynomial, J. Math. Comput. Sci. 7 (2017), 211–229.
BibTeX
@article{Butt2017,
author = {Butt, Saad Ihsan and Khan, Khuram Ali and Pecaric, Josip},
title = {Generalization of Popoviciu type inequalities via Green function and Abel-Gontscharoff interpolating polynomial},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {211--229},
doi = {}
}