Extended Jensen’s functional for diamond integral via Green’s function and Hermite polynomial

Abstract In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension Jensen’s functional for n -convex functions is deduced from inequality involving diamond integrals. Special conditions, including Taylor two point formula Lagrange’s interpolation, are also deployed to find further extensions functional. This paper includes discussion on bounds Grüss inequality, Ostrowski Čebyšev associated newly defined