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On a property of $N$-functions

D. V. Salekhov

Voronezh Engineering-Construction Institute

Abstract: 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 $(\Delta_2)$.

UDC: 517.5

Received: 05.02.1968

 English version: Mathematical Notes, 1968, 4:3, 662–667

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