Popoviciu type inequalities via Green function and Taylor polynomial

Authors

SAAD IHSAN BUTT
KHURAM ALI KHAN
JOSIP PECARIC

Abstract

The well-known Taylor polynomial is used to construct the identities coming from Popoviciu type inequalities for convex functions via the Green function. The bounds for the new identities are found using the Çebyşev functional to develop the Grüss and Ostrowski type inequalities. Further, more exponential convexity together with Cauchy means is presented for linear functionals associated with the obtained inequalities.

DOI

10.3906/mat-1501-38

Keywords

Popoviciu inequality, Taylor formula, Green function, Çebyşev functional, Grüss inequality, Ostrowski inequality, exponential convexity, Cauchy mean

First Page

333

Last Page

349

Recommended Citation

BUTT, SAAD IHSAN; KHAN, KHURAM ALI; and PECARIC, JOSIP (2016) "Popoviciu type inequalities via Green function and Taylor polynomial," Turkish Journal of Mathematics: Vol. 40: No. 2, Article 9. https://doi.org/10.3906/mat-1501-38
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/9