Popoviciu type inequalities for n-convex functions via extension of weighted Montgomery identity

Abstract

In this article, we derive the Popoviciu-type inequalities by using the weighted version of the extension of Montgomery’s identity and Green functions. Some results for n-convex functions at a point are also obtained. Besides that, some Ostrowski-type inequalities are also presented, which are interrelated with the obtained inequalities. Mathematics Subject Classification (2010): 26A51, 26D15, 26D20. Received 26 September 2021; Accepted 13 May 2022