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

Abstract

Extension of Montgomery's identity is used in derivation of Popoviciu-type inequalities containing sums , 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.

Keywords

• n-convex functions
• n-convex functions at a point
• montgomery identity
• čebyšev functional
• exponential convexity.
• primary 26a51
• 26d15
• 26d20.