The improvement of the value distribution on $f+a(f')^{n}$


Shanpeng Zeng, Yan Yang, Yuesheng Wu




Let $f(z)$ be a transcendental meromorphic function in the plane and let $a(\neq 0)$, $b$ be two finite complex numbers. Then for positive integer $n\geq 3$, we have $(n-1)T(r,f')eq3verline{N}(r,f)+4verline{N}(r,\frac{1}{f+a(f')^{n}-b})+S(r,f)$.