Generalizations of Ostrowski type inequalities via Hermite polynomials

Journal of inequalities and applications

article

Ljiljanka Kvesić¹  Josip Pečarić²  Mihaela Ribičić Penava³ 

[1] Faculty of Science and Education, University of Mostar;RUDN University;Department of Mathematics, University of Osijek

关键词: Ostrowski type inequality;    Hermite polynomials;    Montgomery identity;    Grüss inequality;   

DOI  :  10.1186/s13660-020-02441-6

学科分类：电力

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY