Uniqueness of meromorphic function with deficient values (Q2719917)

Suppose that two non-constant meromorphic functions \(f,g\) share two values \(1,\infty\) \(CM\) and a value 0 \(IM\). If \(f\not\equiv g\) and NEWLINE\[NEWLINE2N\left( r,{1\over f-a}\right) +{3\over 2}N_{(2} \left(r, {1\over f}\right) +{3\over 2} N_{(2} \left(r, {1\over g}\right)NEWLINE\]NEWLINE NEWLINE\[NEWLINE<\bigl( \lambda+o(1) \bigr)T(r,f) (r\notin E,\lambda <1,a\neq 0,1,\infty),NEWLINE\]NEWLINE then \(f\neq a\) and one of the following cases holds: (1) \(f\equiv ag\). (2) \(f-(1-a)g\equiv a\), (3) \((f-a)(g+a-1)\equiv a(1-a)\).