Entire functions that share two small functions with their derivatives (Q2743128)

Suppose that \(f\) is a non-constant entire function and \(a,b (\neq \infty)\) are two distinct small functions. If \(f\) and \(f'\) share the small function \(a\) CM, NEWLINE\[NEWLINE\{f-b=0 \text{ and }f'-b'\neq 0\} \subset\{f'-b= 0\text{ and }f''- b'\neq 0\},NEWLINE\]NEWLINE NEWLINE\[NEWLINE\{f-b=0 \text{ and }f'-b'= 0\}\subset \{f'-b =0\text{ and }f''-b' =0\}NEWLINE\]NEWLINE and \(N(r,1/(f-b)) \neq S(r,f)\). Then \(f=f'\).