Extended Jensen's functional for diamond integral via Hermite polynomial (Q1981849)

Summary: In this paper, with the help of Hermite interpolating polynomial, extension of Jensen's functional for \(n\)-convex function is deduced from Jensen's inequality involving diamond integrals. Special Hermite conditions, including Taylor two-point formula and Lagrange's interpolation, are also deployed to find further extensions of Jensen's functional. The paper also includes discussion on bounds for Grüss-type inequality, Ostrowski-type inequality, and Chebyshev functional associated with newly defined Jensen's functional.