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Zbl 0802.26009
Vamanamurthy, M.K.; Vuorinen, M.
Inequalities for means.
(English)
[J] J. Math. Anal. Appl. 183, No.1, 155-166 (1994). ISSN 0022-247X

The authors prove inequalities for power means, Stolarsky means, the geometric mean, and Gauss's arithmetic-geometric mean and establish connections to elliptic integrals. A typical result is that $((x\sp t - y\sp t)/(\ln (x/y)t))\sp{1/t}$ is a continuous function of $t$ and strictly increases from $(xy)\sp{1/2}$ to $\max (x,y)$ as $t$ grows from 0 to $\infty$.
[J.Aczél (Waterloo / Ontario)]
MSC 2000:
*26D15 Inequalities for sums, series and integrals of real functions
33E05 Elliptic functions and integrals
26D07 Inequalities involving other types of real functions
26A24 Differentiation of functions of one real variable

Keywords: Bernoulli-de l'Hospital rule; inequalities; power means; Stolarsky means; geometric mean; Gauss's arithmetic-geometric mean; elliptic integrals

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