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ARITHMETIC MEAN OF VALUES AND VALUE AT MEAN OF ARGUMENTS FOR CONVEX FUNCTIONS

Part of: Inequalities General convexity

Published online by Cambridge University Press:  01 July 2008

CRISTINEL MORTICI
CRISTINEL MORTICI*
Affiliation:
Department of Mathematics, Valahia University of Targoviste, Bd. Unirii 18, Targoviste, Romania (email: cmortici@valahia.ro)
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Abstract

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We give here some extensions of inequalities of Popoviciu and Rado. The idea is to use an inequality [C. P. Niculescu and L. E. Persson, Convex functions. Basic theory and applications (Universitaria Press, Craiova, 2003), Page 4] which gives an approximation of the arithmetic mean of n values of a given convex function in terms of the value at the arithmetic mean of the arguments. We also give more general forms of this inequality by replacing the arithmetic mean with others. Finally we use these inequalities to establish similar inequalities of Popoviciu and Rado type.

Keywords

convex functionsmeansPopoviciu’s inequalityRado’s inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals 52A40: Inequalities and extremum problems
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 1 , July 2008 , pp. 137 - 141
Copyright
Copyright © Australian Mathematical Society 2008

References

[1]Mitrinović, D. S., Pečarić, J. E. and Fink, A. M., Classical and new inequalities in analysis (Kluwer Academic Publishers, Dordrecht, 1993).CrossRefGoogle Scholar
[2]Niculescu, C. P. and Persson, L. E., Convex functions. Basic theory and applications (Universitaria Press, Craiova, 2003).Google Scholar