Journal of Function Spaces (Jan 2021)
Extended Jensen’s Functional for Diamond Integral via Hermite Polynomial
Abstract
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 C˘ebyšev functional associated with newly defined Jensen’s functional.