Geodesic
On a property of $N$-functions
Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 281-290

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We consider three classes of $N$-functions: $(\Delta')$, the class of functions satisfuing the $\Delta'$ condition, $(\Delta_2)$, the class of functions satisfuing the $\Delta_2$ condition, and $(M_\Delta)$, the class of functions $M(u)$ satisfying the condition: $\lim\limits_{u\to\infty}\ln M(u)/\ln u =p\infty$. We establish the connection between the class of powers and the class of $N$-functions $M(u)$ which belong to the class $(\Delta')$ together with their complementary functions and we also establish the connections between the classes $(\Delta')$, $(M_\Delta)$ and $(\Delta_2)$. 
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     author = {D. V. Salekhov},
     title = {On a property of $N$-functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {281--290},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a3/}
}
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D. V. Salekhov. On a property of $N$-functions. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 281-290. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a3/