Then g z)=m z exp^{l z)}, (3.11) where (l z)) is a polynomial such that (rho(g)=deg l z)>1), and (m z)) is a meromorphic function such that (rho(m)
For a meromophic function f, we use the basic notations of the Nevanlinna theory of meromorphic functions such as (T r,f)), (m r,f)), (N r,f)) and (overline{N}(r,f)) as explained in [11 13].
We shall use the standard notations in Nevanlinna's value distribution theory of meromorphic functions such as,, and (see, e.g., [1, 2]).
We assume that the reader is familiar with the standard notations and results in Nevanlinna's value distribution theory of meromorphic functions such as the characteristic function, proximity function, counting function, the first and second main theorems (see, e.g., [1 4]).
We adopt the standard notations of the Nevanlinna value distribution theory of meromorphic functions such as T ( r, f ), m ( r, f ) and N ( r, f ) as explained in [1 3].
We use the basic notations of the Nevanlinna theory of meromorphic functions such as T ( r, f ), m ( r, f ), N ( r, f ) and N ¯ ( r, f ) as explained in [1 3].
For a meromorphic function f z), we define its shift by f z + c), and define its difference operators by Δ c f ( z ) = f ( z + c ) - f ( z ) and Δ c n f ( z ) = Δ c n - 1 ( Δ c f ( z ) ), n ∈ ℕ, n ≥ 2. We adopt the standard notations of the Nevanlinna theory of meromorphic functions such as T r, f), m r, f), N r, f) and N ¯ ( r, f ) as explained in [1 3].
Theorem B Let f be a nonconstant meromorphic function such that N ¯ ( r, f ) + N ( r, 1 f ′ ) < ( λ + o ( 1 ) ) T ( r, f ′ ) for λ ∈ ( 0, 1 2 ).
Theorem C Let f be a nonconstant meromorphic function such that N ¯ ( r, f ) + N ¯ ( r, 1 f ′ ) < ( λ + o ( 1 ) ) T ( r, f ′ ) for λ ∈ ( 0, 1 2 ).
Let f ( z ) be a transcendental meromorphic function such that its order of growth ρ ( f ) is not an integer or infinite, and let c ∈ C be a constant such that f ( z + c ) ≢ f ( z ).
Let f 1, f 2, f 3 be meromorphic functions such that f 1 is not a constant.
