Generalization of Popoviciu-Type Inequalities Via Fink’s Identity

We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev fun...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 13; no. 4; pp. 1495 - 1511
Main Authors Butt, Saad Ihsan, Pečarić, Josip, Vukelić, Ana
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2016
Subjects
Mathematics
Mathematics and Statistics
Fink’s identity
Primary 26D07
26D20
Grüss inequality
divided difference
Ostrowski inequality
Čebyšev functional
26D99
Convex function
26D15
exponential convexity
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Summary:We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results relating to the Grüss- and Ostrowski-type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-015-0573-8