On a Problem of Krasnosel'skii and Rutickii

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.