Let $f,g:(0,\infty)\rightarrow (0,\infty)$ be right-continuous decreasing functions. Assume that $$\frac{\inf_{s>0} s+t \cdot f(s) }{\inf_{s>0}s+t\cdot g(s)}<1$$ for all $t>0$. Find a positive number $C$ such that $$f(s)<C\cdot g(s/C)$$ for all $s$.
2026-04-06 03:39:58.1775446798
Find a positive number $C$ such that $f(s)<C\cdot g(s/C)$ for all $s$
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