Generalizations of the Jensen functional involving diamond integrals via Abel–Gontscharoff interpolation

Abstract

Abstract In this paper we obtain several refinements of the Jensen inequality on time scales by generalizing Jensen’s functional for n-convex functions. We also investigate the bounds for the identities related to the new improvements obtained.

Keywords

• Time-scales calculus
• Abel–Gontscharoff’s interpolation polynomial
• Jensen’s inequality
• Green function