<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, generalizations of Steffensen’s inequality with bounds involving any two subintervals motivated by Cerone’s generalizations are given. Furthermore, weaker conditions for Cerone’s generalization as well as for new generalizations obtained in this paper are given. Moreover, functionals defined as the difference between the left-hand and the right-hand side of these generalizations are studied and new Stolarsky type means related to them are obtained.</p></abstract>

In this paper, generalizations of Steffensen’s inequality with bounds involving any two subintervals motivated by Cerone’s generalizations are given. Furthermore, weaker conditions for Cerone’s generalization as well as for new generalizations obtained in this paper are given. Moreover, functionals defined as the difference between the left-hand and the right-hand side of these generalizations are studied and new Stolarsky type means related to them are obtained.

Cerone’s Generalizations of Steffensen’s Inequality

Faculty of Textile Technology University of Zagreb Prilaz baruna Filipovića 28a 10000 Zagreb CROATIA

Anamarija Perušić Faculty of Civil Engineering University of Rijeka Radmile Matejčić 3 51000 Rijeka CROATIA

Ksenija Smoljak Faculty of Textile Technology University of Zagreb Prilaz baruna Filipovića 28a 10000 Zagreb CROATIA

Tatra Mountains Mathematical Publications

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

{"article-title":"Cerone\u2019s Generalizations of Steffensen\u2019s Inequality"}

In this paper, generalizations of Steffensen’s inequality with bounds involving any two subintervals motivated by Cerone’s generalizations are given....

Cerone’s Generalizations of Steffensen’s Inequality

Published Online: Aug 15, 2014

Page range: 53 - 75

Received: Sep 09, 2013

DOI: https://doi.org/10.2478/tmmp-2014-0006

Keywords
Steffensen inequality, monotonic functions, weaker conditions, exponential convexity, Stolarsky type means

© 2014

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

Cerone’s Generalizations of Steffensen’s Inequality

Published Online: Aug 15, 2014

Page range: 53 - 75

Received: Sep 09, 2013

DOI: https://doi.org/10.2478/tmmp-2014-0006

KeywordsSteffensen inequality, monotonic functions, weaker conditions, exponential convexity, Stolarsky type means

© 2014

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

Keywords
Steffensen inequality, monotonic functions, weaker conditions, exponential convexity, Stolarsky type means