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Popoviciu type inequalities for n-convex functions via extension of Montgomery identity

inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform., 39 (1) (2012), 65-75. [9] J. Pečarić, M. Praljak and A. Witkowski, Linear operator inequality for n-convex functions at a point, Math. Ineq. Appl. 18 (2015), 1201-1217. [10] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, New York, 1992. [11] T. Popoviciu, Notes sur les fonctions convexes d'orde superieur III, Mathematica (Cluj) 16, (1940), 74-86. [12] T

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Generalizations of Steffensen’s inequality via two-point Abel-Gontscharoff polynomial

Abstract

Using two-point Abel-Gontscharoff interpolating polynomial some new generalizations of Steffensen’s inequality for n−convex functions are obtained and some Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using the Čebyšev functional some new bounds for the remainder in obtained generalizations are proven and related Grüss-type inequalities are given.

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Generalizations of Steffensen’s inequality via some Euler-type identities

Abstract

Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.

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