Abstract
AbstractWe present new generalizations of the weighted Montgomery identity constructed by using the Hermite interpolating polynomial. The obtained identities are used to establish new generalizations of weighted Ostrowski type inequalities for differentiable functions of class $C^{n}$
C
n
. Also, we consider new bounds for the remainder of the obtained identities by using the Chebyshev functional and certain Grüss type inequalities for this functional. By applying those results we derive inequalities for the class of n-convex functions.
Funder
Sveučilište Josipa Jurja Strossmayera u Osijeku
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference18 articles.
1. Agarwal, R.P., Wong, P.J.Y.: Error Inequalities in Polynomial Interpolation and Their Applications. Kluwer Academic, Dordrecht (1993)
2. Aglić Aljinović, A., Čivljak, A., Kovač, S., Pečarić, J., Ribičić Penava, M.: General Integral Identities and Related Inequalities. Element, Zagreb (2013)
3. Aglić Aljinović, A., Pečarić, J., Vukelić, A.: On some Ostrowski type inequalities via Montgomery identity and Taylor’s formula II. Tamkang J. Math. 36(4), 279–301 (2005)
4. Awan, K.M., Pečarić, J., Ribičić Penava, M.: Companion inequalities to Ostrowski–Grüss type inequality and applications. Turk. J. Math. 39, 228–234 (2015)
5. Cerone, P., Dragomir, S.S.: Some new Ostrowski-type bounds for the Čebyšev functional and applications. J. Math. Inequal. 8(1), 159–170 (2014)
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