A NOTE ON THE VALUE DISTRIBUTION OF f2(f')nFOR n≥2
Yan Jiang · Bulletin of the Korean Mathematical Society · 2016
Let f be a transcendental meromorphic function in the complex plane $\mathbb{C}$ , and a be a nonzero constant. We give a quantitative estimate of the characteristic function T(r, f) in terms of $N(r,1/(f^2(f^{\prime})^n-a))$ , which states as following inequality, for positive integers $n{\geq}2$ , $$T(r,f){\leq}\(3+{\frac{6}{n-1}}\)N\(r,{\frac{1}{af^2(f^{\prime})^n-1}}\)+S(r,f)$$ .