engleski

Generalization of Popoviciu-Type Inequalities Via Fink’s Identity

We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results relating to the Gr\" uss and Ostrowski type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities.

Convex function; divided difference; Fink’s identity; Čebyšev functional; Gr\

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