Generalizations of Ostrowski type inequalities via Hermite polynomials

We 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 . Also, we consider new bo...

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Veröffentlicht in:Journal of inequalities and applications 2020-06, Vol.2020 (1), p.1-14, Article 176
Hauptverfasser: Kvesić, Ljiljanka, Pečarić, Josip, Ribičić Penava, Mihaela
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Sprache:eng
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Zusammenfassung:We 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 . 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.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02441-6