On the uniqueness of meromorphic functions that share two sets (Q2752634)

Let \(S=\{\omega: \omega^7-42\omega^2+70\omega-30=0\}\) and \(k\) be an integer such that \(k\geq 3\). Suppose \(f\) and \(g\) are two non-constant meromorphic functions such that \(\min\{\Theta(\infty,f),\Theta(\infty,g)\}>{1\over2}\). If \(E_{k)}(S,f)=E_{k)}(S,g)\), and \(E(\{\infty\},f)=E(\{\infty\},g)\), then \(f\equiv g\).