Ciara Mcdaniel

2022-07-16

Is there any relationship similar to the following. Let $X$ be the maximum of functions ${f}_{1}\left(x\right)+{f}_{2}\left(x\right)$. Let ${X}_{1}$ be a maximum of ${f}_{1}\left(x\right)$ and let ${X}_{2}$ be a maximum of ${f}_{2}\left(x\right)$. Is there any relationship between $X$ and ${X}_{1}$ and ${X}_{2}$?

For example can we say under what condition will $X$ be in-between ${X}_{1}$ and ${X}_{2}$, ${X}_{1}\le X\le {X}_{2}$.

Any reference would be greatly appreciated.

Expert

$max\left(f+g\right)\le maxf+maxg$