Meromorphic Functions That Share Fixed-Points
Copyright policy )Meromorphic Functions That Share Fixed-Points
Let \(f(z)\) and \(g(z)\) be two meromorphic functions, \(n\geq 11\). If \(f^n(z) f'(z)- z\) and \(g^n(z) g'(z)- z\) assume the same zeros with the same multiplicities, then either \[ f(z)= c_1 e^{cz^2},\quad g(z)= c_2 e^{-cz^2}\quad (4(c_1 c_2)^{n+ 1}C^2= -1) \] or \[ f(z)= tg(z)\qquad (t^{n+1}= 1). \] {}.
- State Key Laboratory of Millimeter Waves China (People's Republic of)
- Southeast University China (People's Republic of)
differential polynomial, fixed point, Applied Mathematics, uniqueness, meromorphic function, fixed-point, Meromorphic functions of one complex variable (general theory), uniqueness theorem, Analysis, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
differential polynomial, fixed point, Applied Mathematics, uniqueness, meromorphic function, fixed-point, Meromorphic functions of one complex variable (general theory), uniqueness theorem, Analysis, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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