Geodesic
A general class of inequalities with mixed means
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 864-872.

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Suppose $(T,\Sigma,\mu)$ is a space with positive measure, $f\colon\mathbb R\to\mathbb R$ is a strictly monotone continuous function, and $\mathfrak G(T)$ is the set of real $\mu$-measurable functions on $T$. Let $x(\cdot)\in\mathfrak G(T)$ and $(f\circ x)(\cdot)\in L_1(T,\mu)$. Comparison theorems are proved for the means $\mathfrak M_{(T,\mu,f)}\bigl (x(\cdot)\bigr)$ and the mixed means $\mathfrak M_{(T_1,\mu _1,f_1)}\bigl(\mathfrak M_{(T_2,\mu_2,f_2)}\bigl(x(\cdot)\bigr)\bigr)$ these inequalities imply analogs and generalizations of some classical inequalities, namely those of Hölder, Minkowski, Bellman, Pearson, Godunova and Levin, Steffensen, Marshall and Olkin, and others. These results are a continuation of the author's studies. 
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     title = {A general class of inequalities with mixed means},
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     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a6/}
}
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R. Kh. Sadikova. A general class of inequalities with mixed means. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 864-872. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a6/

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