Cerone’s Generalizations of Steffensen’s Inequality

Josip Pečarić; Anamarija Perušić; Ksenija Smoljak

doi:10.2478/tmmp-2014-0006

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Cerone’s Generalizations of Steffensen’s Inequality

Tatra Mountains Mathematical Publications

Volume 58 (2014): Issue 1 (March 2014)

By: Josip Pečarić, Anamarija Perušić and Ksenija Smoljak

Open Access

|Aug 2014

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2014-0006 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 53 - 75

Submitted on: Sep 9, 2013

Published on: Aug 15, 2014

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Steffensen inequality,

monotonic functions,

weaker conditions,

exponential convexity,

Stolarsky type means

Related subjects:

Mathematics,

General mathematics

© 2014 Josip Pečarić, Anamarija Perušić, Ksenija Smoljak, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 58 (2014): Issue 1 (March 2014)