<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Using Euler-type identities some new generalizations of Steffensen’s inequality for <italic>n</italic>–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.</p></abstract>

Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.

Generalizations of Steffensen’s inequality via some Euler-type identities

Faculty of Textile Technology, University of Zagreb, Croatia

Faculty of Civil Engineering, University of Rijeka, Croatia

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Generalizations of Steffensen\u2019s inequality via some Euler-type identities"}

Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities...

Generalizations of Steffensen’s inequality via some Euler-type identities

Published Online: Aug 02, 2016

Page range: 103 - 126

Received: Oct 14, 2014

DOI: https://doi.org/10.1515/ausm-2016-0007

Keywords
Steffensen’s inequality, Euler-type identities, Bernoulli polynomials, Ostrowski-type inequalities, Čebyšev functional

© 2016 Josip Pečarić et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Generalizations of Steffensen’s inequality via some Euler-type identities

Published Online: Aug 02, 2016

Page range: 103 - 126

Received: Oct 14, 2014

DOI: https://doi.org/10.1515/ausm-2016-0007

KeywordsSteffensen’s inequality, Euler-type identities, Bernoulli polynomials, Ostrowski-type inequalities, Čebyšev functional

© 2016 Josip Pečarić et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Steffensen’s inequality, Euler-type identities, Bernoulli polynomials, Ostrowski-type inequalities, Čebyšev functional