Abstract

BARCENAS, DIOMEDES  and  FINOL, CARLOS. On a Problem of Krasnosel'skii and Rutickii. Rev.colomb.mat. [online]. 2011, vol.45, n.2, pp.179-186. ISSN 0034-7426.

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.

Keywords : Orlicz Functions; N-Functions; Submultiplicative Functions; Matuszewska--Orlicz indices.

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