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Generalization of Jensen's and Jensen- Steffensen's inequalities and their converses by Hermite's polynomial and majorization theorem

In this paper, using majorization theorems and Hermite's interpolating polynomials we obtain results concerning Jensen's and Jensen- Steffensen's inequalities and their converses in both the integral and the discrete case. We give bounds for identities related to these inequalities by using \v{; ; ; C}; ; ; eby\v{; ; ; s}; ; ; ev functionals. We also give Gr{; ; ; \"u}; ; ; ss type inequalities and Ostrowsky type inequalities for these functionals.

Majorization ; Green function ; Jensen inequality ; Jensen-Steffensen inequality ; Hermite interpolating polynomial ; $n$-convex function ; \v{; ; ; C}; ; ; eby\v{; ; ; s}; ; ; ev functional ; Gr{; ; ; \

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