Generalizations of Steffensen's inequality by Lidstone's polynomial and related results

In this paper we obtain few valuable identities by using Lidstone's polynomial. Further, the identities were applied for constructing new generalizations of Steffensen's inequality, namely for (2n)−convex and (2n + 1)−convex functions. In addition, using Čebyšev and Grüss type inequalities...

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Published inQuaestiones mathematicae Vol. 43; no. 3; pp. 293 - 307
Main Authors Pečarić, Josip, Perušić Pribanić, Anamarija, Vukelić, Ana
Format Journal Article
LanguageEnglish
Published Grahamstown Taylor & Francis 03.03.2020
Taylor & Francis Ltd
Subjects
generalizations
Grüss-type inequality
Identities
Inequalities
Lidstone polynomial
Mathematical analysis
n-convex functions
Ostrowski-type inequality
Polynomials
Primary 26D15
Secondary 26A51
Steffensen's inequality
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Summary:In this paper we obtain few valuable identities by using Lidstone's polynomial. Further, the identities were applied for constructing new generalizations of Steffensen's inequality, namely for (2n)−convex and (2n + 1)−convex functions. In addition, using Čebyšev and Grüss type inequalities we consider the bounds for the integrals in the perturben versions of the previously described identities. Moreover, related Ostrowski type inequalities are given.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2018.1539048