Suppose I have three functions $f(z):\mathbb{C}\rightarrow\mathbb{C}$, $g(z):\mathbb{C}\rightarrow\mathbb{C}$, and $h(z):\mathbb{C}\rightarrow\mathbb{C}$.
What methods work for finding all $z$ such that $f(z)=g(z)=h(z)$? Variants of Newton-Raphson are acceptable, but I'm having difficulty encoding it.