An Elementary Proof of the Mean Inequalities

Ilhan M. Izmirli^{*}

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References

[1] G. H. Hardy, J. E. Littlewood and G. Polya, “Inequalities,” 2nd Edition, Cambridge University Press, London, 1964.

[2] B. C. Carlson, “A Hypergeometric Mean Value,” Proceedings of the American Mathematical Society, Vol. 16, No. 4, 1965, pp. 759-766.
doi:10.1090/S0002-9939-1965-0179389-6

[3] B. C. Carlson and M. D. Tobey, “A Property of the Hypergeometric Mean Value,” Proceedings of the American Mathematical Society, Vol. 19, No. 2, 1968, pp. 255-262.
doi:10.1090/S0002-9939-1968-0222349-X

[4] E. F. Beckenbach and R. Bellman, “Inequalities,” 3rd Edition, Springer-Verlag, Berlin and New York, 1971.

[5] H. Alzer, “übereinen Wert, der zwischendemgeometrischen und demartihmetischen Mittelzweier Zahlenliegt,” Elemente der Mathematik, Vol. 40, 1985, pp. 22-24.

[6] H. Alzer, “Ungleichungenfür (e/a)^{a}(b/e)^{b} ,” Elemente der Mathematik, Vol. 40, 1985, pp. 120-123.