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Original scientific paper

Weighted Popoviciu type inequalities via generalized Montgomery identities

Saad Ihsan Butt ; Department of Mathematics, COMSATS, Institute of Information Technology, Lahore, Pakistan
Josip Pečarić ; Department of Mathematics, Faculty of Textile Technology, University of Zagreb, 10 000 Zagreb, Croatia

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page 69-89

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We obtained useful identities via generalized Montgomery identities, 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 Grüss and Ostrowski type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functionals associated with the obtained inequalities.


Convex function, divided difference, generalized Montgomery identity, Čebyšev functional, Grüss inequality, Ostrowski inequality, exponential convexity

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