The question is self-explanatory, I need to find the proximal mapping of $\frac{1}{2} \Vert Ax - b \Vert_2^2$ where $A$ in a given rectangular matrix and $b$ is a given vector of appropriate size.
Please note that I don't need any proof or justification whatsoever, just naming the proximal mapping would suffice, albeit perhaps kindly with a credible reference. Thank you for your time!
Hint: Given $y$, the proximal map at $y$ is the unique minimizer of the function $$x\mapsto \tfrac{1}{2}\|Ax-b\|_2^2 + \tfrac{1}{2}\|x-y\|_2^2.$$ Do you know how to take the derivative of this function, set it equal to $0$, and solve for $x$?
As for references, check the books by Beck and by Bauschke-Combettes.