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Generalisation of the arithmetic mean – geometric mean – harmonic mean inequality

Published online by Cambridge University Press:  01 August 2016

Zbigniew Urmanin
Zbigniew Urmanin*
Affiliation:
Buchenstr. 6, 49740 Haselünne, Germany
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Abstract

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Information
The Mathematical Gazette , Volume 86 , Issue 506 , July 2002 , pp. 293 - 296
Copyright
Copyright © The Mathematical Association 2002

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References

1. Beckenbach, E.F., Bellman, R., Inequalities, Springer, Berlin, New York (1971).Google Scholar
2. Bullen, P.S.. Mitrinović, D.S. and Vasić, P.M., Means and their inequalities, Reidel, Dordrecht (1988).Google Scholar
3. Hardy, G.H., Littlewood, J.E. and Pólya, G., Inequalities, Cambridge (1967).Google Scholar
4. Kazarinoff, N.D., Analytic inequalities, New York, London (1964).Google Scholar
5. Mitrinović, D.S., Analytic inequalities, Springer, New York, Heidelberg (1970).Google Scholar
6. Mitrinović, D.S., Pečarić, J.E. and Fink, A.M., Classical and new inequalities in analysis, Kluwer, Dordrecht (1993).Google Scholar
7. Urmanin, Z., Eine einheitliche Untersuchungsmethode der Potenz-, Exponential- und Logarithmusfunktion Google Scholar
Teil 1: Die Potenzfunktion, Praxis der Mathematik 43 (2001) pp. 23–26.Google Scholar
Teil 2: Die Exponentialfunktion, Praxis der Mathematik 43 (2001) pp. 181–184.Google Scholar
Teil 3: Die Logarithmusfunktion (to appear).Google Scholar
8. Urmanin, Z., An inductive proof of the arithmetic mean – geometric mean inequality, Math. Gaz. 84 (March 2000) pp. 101–102.CrossRefGoogle Scholar
9. Hlawka, E., Ungleichungen, MANZ Verlag, Wien (1990).Google Scholar
10. Lucht, L.G., On the arithmetic – geometric mean inequality, Amer. Math. Monthly 102 (1995) pp. 739–740.Google Scholar
11. Alzer, H., A proof of the arithmetic mean – geometric mean inequality, Amer. Math. Monthly 103 (1996) p. 585.CrossRefGoogle Scholar