Abstract
AbstractIn this paper, first we present some interesting identities associated with Green’s functions and Fink’s identity, and further we present some interesting inequalities for r-convex functions. We also present refinements of some Hardy–Littlewood–Pólya type inequalities and give an application to the Shannon entropy. Furthermore, we use the Čebyšev functional and Grüss type inequalities and present the bounds for the remainder in the obtained identities. Finally, we use the obtained identities together with Hölder’s inequality for integrals and present Ostrowski type inequalities.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference23 articles.
1. Bennett, G.: Lower bounds for matrices. Linear Algebra Appl. 82, 81–98 (1986)
2. Cerone, P., Dragomir, S.S.: Some new Ostrowski-type bounds for the Čebyšev functional and applications. J. Math. Inequal. 8(1), 159–170 (2014)
3. Chebyshev, P.L.: Sur les expressions approximative des integrals par les auters prises entre les mêmes limites. Proc. Math. Soc. Charkov. 2, 93–98 (1882)
4. Fahad, A., Pečarić, J., Qureshi, M.I.: Generalized Steffensen’s inequality by Lidstone interpolation and Montogomery’s identity. J. Inequal. Appl. 2018, 237, 1–21 (2018)
5. Fink, A.M.: Bounds of the deviation of a function from its averages. Czechoslov. Math. J. 42(117), 289–310 (1992)