Generalizations of Ostrowski type inequalities via Hermite polynomials

被引：1

作者：

Kvesic, Ljiljanka ^{[1
]}

Pecaric, Josip ^{[2
]}

Penava, Mihaela Ribicic ^{[3
]}

机构：

[1] Univ Mostar, Fac Sci & Educ, Matice Hratske Bb, Mostar 88000, Bosnia & Herceg

[2] RUDN Univ, Miklukho Maklaya Str 6, Moscow 117198, Russia

[3] Univ Osijek, Dept Math, Trg Ljudevita Gaja 6, Osijek 31000, Croatia

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2020年 / 2020卷 / 01期

关键词：

Ostrowski type inequality; Hermite polynomials; Montgomery identity; Gruss inequality;

D O I：

10.1186/s13660-020-02441-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 Gruss type inequalities for this functional. By applying those results we derive inequalities for the class ofn-convex functions.

引用

页数：14

共 18 条

[11] Latif MA, 2017, INT J ANAL APPL, V13, P1
[12] Gruss and Ostrowski type inequalities
Niezgoda, Marek
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (23) : 9779 - 9789
[13] Ostrowski A., 1938, Comment Math. Helv., V10, P226
[14] Peari J., 1980, B I POLITEH TIMISOAR, V25, P10
[15] Peari J.E., 1992, Convex Functions, Partial Orderings, and Statistical Applications
[16] Bounds for the Chebyshev functional and applications to the weighted integral formulae
Pecaric, J.
Penava, M. Ribicic
Vukelic, A.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 268 : 957 - 965
[17] Pecaric J, 2020, J INEQUAL SPEC FUNCT, V11, P12
[18] Popoviciu T., 1934, MATH CLUJ, V10, P49

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