Let $F\subseteq (\mathbb R \to\mathbb R)$ be some space of functions, and let $G:F\to \mathbb R$ be a functional. I have a statement of the following form: $$\begin{align}\text{Let } &f^*(x):=x^2. \quad\quad\quad \text{Then }\\ &f^*\in \arg\max_{f\in F} G(f) \end{align}$$
Rather than first defining a function and then referencing it, I'd like to compress this into one equation for brevity's sake. Something like:
$$(x\mapsto x^2)\in \arg\max_{f\in F} G(f)$$
Is there a generally accepted notation like this? I'd prefer not to invent something new and unknown.