Normal Function Concerning Differential In Meromorphic Functions And Shared Values

Our paper mainly study the connection between the differential polynomial in f and shared values, and then we obtain a new normal function: Let F be a family of meromorphic functions on the unit discâ–³, all of whose zeros have multiplicity at least k and there exists a positive number A ≥ 1, such that |f^k(z)| ≤ A whenever f(z) = 0, f ∈ F. Let a₁(z), a₂(z), …, a_k(z) be analytic in D and they are not identical to zero. We write F(z) = f^k)(z) + a₁(z)f^k-1(z) + … + a_k(z)f(z) as a differential polynomial in f(z), and then if for any f ∈ F, f(z) ∈ {a, b} F(z) ∈ {a,b}, where a, b are two distinct finite nonzero complex numbers, then there exists a positive number M = M(a,b), such that for every f ∈ F,where M only depends on a and b.