¹Universidad de Los Ándes, Mérida, Venezuela. Email: null
²Universidad Central de Venezuela, Caracas, Venezuela. Email: carlos.finol@ciens.ucv.ve

In [5,p. 30], M. A. Krasnosel'skii and Ya. B. Rutickii proposed a problem, which can be reformulated as follows. Let f be an N-function such that f(ts)≤ f(t)f(s), s,t≥ 1. Is there another N-function F such that F(st)≤ F(t)F(s), s,t>0 and equivalent to f on [1,∞)?. We give a necessary and sufficient condition for a positive and constructive solution.

Key words: Orlicz Functions, N-Functions, Submultiplicative Functions, Matuszewska--Orlicz indices.

En [5,p. 30], M. A. Krasnosel'skii y Ya. B. Rutickii proponen un problema, el cual puede ser reformulado de la siguiente manera: Sea f una N-función tal que f(ts)≤ f(t)f(s) para todo t,s≥ 1. ¿Existe alguna función F tal que F(st)≤ F(s)F(t), s,t≥ 0, que sea equivalente a f en [1,∞)?. En este articulo, damos una condición necesaria y suficiente para una solución positiva y constructiva.

Palabras clave: Funciones de Orlicz, N-funciones, funciones submultiplicativas, indices de Matuszewska--Orlicz.

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References

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