Suppose we have $\langle p, f(p)\rangle = h(p)$, where $p$ belongs to the $n>1$ dimensional simplex $\Delta$. Suppose that $f$ is continuously differentiable, and $h$ is known for $p\in \Delta$. Is it possible to solve for $f(p)$? Is there a unique solution to $f$?
2026-05-02 06:52:50.1777704770
Solution to $\langle p, f(p)\rangle = h(p)$ for known $h$?
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