Новая и новейшая история.
Федеральное государственное бюджетное учреждение "Российская академия наук".
Том 65.
2021.
С. 93-108
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 Čebyšev functional associated with newly defined Jensen's functional. © 2021 Rabia Bibi et al.