In part of a larger problem, I have shown that I have a function $f$ which satisfies \begin{align*} f\left(\frac{1}{x}\right) = \sqrt{x}f(x), \;\; x>0. \end{align*} I am just wondering if such a relationship has a specific name, as it's existence in my problem yields some rather nice results, and I would like a more elegant way to refer to it.
Thanks in advance.