Complex meromorphic functions $$f'P'(f)$$ and $$g'P'(g)$$ sharing small function with finite weight

2021 ◽  
Author(s):  
Pulak Sahoo ◽  
Samar Halder
Keyword(s):  
Meromorphic Functions ◽  
Small Function

scholarly journals Uniqueness of meromorphic functions sharing one small function

2014 ◽  
Vol 263 ◽  
pp. 225-235
Author(s):  
Li Rui Jie ◽  
Qiu Ling ◽  
Xuan Zuxing
Keyword(s):  
Meromorphic Functions ◽  
Small Function

scholarly journals Meromorphic Functions Sharing a Small Function

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Songmin Wang ◽  
Zongsheng Gao
Keyword(s):  
Positive Integer ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Small Function

We will study meromorphic functions that share a small function, and prove the following result: letf(z)andg(z)be two transcendental meromorphic functions in the complex plane and letn≥11be a positive integer. Assume thata(z)(≢0)is a common small function with respect tof(z)andg(z). Iffnf′andgng′sharea(z)CM, then eitherfn(z)f′(z)gn(z)g′(z)≡a2(z), orf(z)≡tg(z)for a constant satisfyingtn+1=1. As applications, we give several examples.

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