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

Abstract

Extension of Montgomery's identity is used in derivation of Popoviciutype inequalities containing sums m i=1 pif (xi), where f is an n-convex function.Integral analogues and some related results for n-convex functions at a point are also given, as well as Ostrowski-type bounds for the integral remainders of identities associated with the obtained inequalities.

On Ostrowski Type Inequalities via the Extended Version of Montgomery’s Identity

“…Proof. By taking the difference of identities (4) and (6) we get (5). After some rearrangements we get…”

Positivity of sums and integrals for n-convex functions via the Fink identity

“…Remark 5.4 Using the same method as in [2], we can construct new families of exponentially convex functions and Cauchy type means. Also, using the idea described in [2] we can obtain results for the n−convex functions at a point.…”

Weighted majorization inequalities for n-convex functions via extension of Montgomery identity using Green function

“…Remark 4.4 Using the same method as in [8], we can construct new families of exponentially convex functions and Cauchy type means (see also [2]). Also, using the idea described in [8] we can obtain the results for n-convex functions at point.…”