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101.07 Cauchy's mean value theorem meets the logarithmic mean

Published online by Cambridge University Press:  03 February 2017

Peter R. Mercer*
Affiliation:
Dept. Mathematics, Buffalo State College, Buffalo NY 14221 USA e-mail: mercerpr@buffalostate.edu

Abstract

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Type
Notes
Copyright
Copyright © Mathematical Association 2017 

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References

1. Rademacher, H. & Toeplitz, O., The enjoyment of math, Princeton University Press (1966).Google Scholar
2. Schwenk, A. J., Selection of a fair currency exchange rate. College Math. J. 13 (1982) pp. 154155.Google Scholar
3. Gallant, C., Proof without words: a truly geometric inequality, Math. Mag. 50 (1977) p. 98.Google Scholar
4. Ostle, B. & Terwilliger, H. L., A comparison of two means, Proc. Montana Acad. Sci. 17 (1957) pp. 6970.Google Scholar
5. Polya, G. and Szegö, G., Isoperimetric inequalities in mathematical physics, Princeton University Press (1951).Google Scholar
6. Bruce, I., The logarithmic mean, Math. Gaz. 81 (March 1997) pp. 8992.CrossRefGoogle Scholar
7. Burk, F., By all means, Amer. Math. Monthly 107 (1985) p. 50.Google Scholar
8. Burk, F., The geometric, logarithmic, and arithmetic mean inequality. Amer. Math. Monthly 94 (1987) pp. 527528.Google Scholar
9. Mercer, P. R., More calculus of a single variable, Springer, New York, (2014).Google Scholar
10. Hardy, G. H., Littlewood, J. E. & Polya, G., Inequalities, Cambridge University Press (1967).Google Scholar
11. Carlson, B. C., The logarithmic mean, Amer. Math. Monthly 79 (1972) pp. 615618.Google Scholar
12. Leach, E. B. & Sholander, M. C., Extended mean values II, J. Math. Anal. Appl. 92 (1983) pp. 207223.Google Scholar
13. Lin, T. P., The power mean and the logarithmic mean, Amer. Math. Monthly 81 (1974) pp. 879883.Google Scholar
14. Mao, Q. J., Power mean, logarithmic mean and Heronian dual mean of two positive numbers, J. Suzhou College of Education 16 (1999) pp. 8285 (Chinese).Google Scholar