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INEQUALITIES FOR DRAGOMIR’S MAPPINGS VIA STIELTJES INTEGRALS

Part of: Inequalities Real functions Functions of several variables

Published online by Cambridge University Press:  16 January 2020

TOMASZ SZOSTOK Open the ORCID record for TOMASZ SZOSTOK [Opens in a new window]
TOMASZ SZOSTOK*
Affiliation:
Institute of Mathematics, University of Silesia in Katowice, Bankowa 14, 40-007Katowice, Poland email [email protected]
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Abstract

We present some inequalities for the mappings defined by Dragomir [‘Two mappings in connection to Hadamard’s inequalities’, J. Math. Anal. Appl.167 (1992), 49–56]. We analyse known inequalities connected with these mappings using a recently developed method connected with stochastic orderings and Stieltjes integrals. We show that some of these results are optimal and others may be substantially improved.

Keywords

convex functionHermite–Hadamard inequalitystochastic orderStieltjes integral

MSC classification

Primary: 26A51: Convexity, generalizations
Secondary: 26B25: Convexity, generalizations 26D10: Inequalities involving derivatives and differential and integral operators 39B62: Functional inequalities, including subadditivity, convexity, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 240 - 250
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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