Let be a meromorphic function with order and let be a fixed nonzero complex number, then for each one has (2.7).
Let (f z)) be a meromorphic function of order (sigma=sigma(f), sigma be a fixed nonzero complex number.
Let f ( z ) be a meromorphic function with order σ = σ ( f ), σ < + ∞, and let η be a fixed nonzero complex number, then, for each ε > 0, we have T ( r, f ( z + η ) ) = T ( r, f ) + O ( r σ − 1 + ε ) + O ( log r ).
Let (f z)) be a meromorphic function with order (sigma=sigma(f)be a fixed nonzero complex number, then for each (varepsilon>0), we have Tbigl r,f z+eta bigr)=T r,f +Obigl(r^{sigma-1+varepsilon}bigr)+O log r).
Let (f z)) be a meromorphic function with order (sigma=sigma(f)), (sigma<+infty), and let c be a fixed nonzero complex number, then for each (varepsilon > 0), we have Tbigl r,f z + c bigr)=T (r, f)+Obigl(r^{sigma-1+varepsilon}bigr)+O log r).
Let f ( z ) be a meromorphic function of finite order σ, and let η be a fixed nonzero complex number, then, for each ε > 0, we have m ( r, f ( z + c ) f ( z ) ) + m ( r, f ( z ) f ( z + c ) ) = O ( r σ − 1 + ε ).
where a, b are fixed nonzero reals with a2 + b2 ≠ 1.
For a given mapping (f : V to Y), we use the abbreviations begin{aligned}& D_{1} f x,y) := f(ax+by) - af(x) - bf y), & D_{2} f x,y) := f(ax+by) + abf x-y) - abf x-yf(x) - b(a+b) f(y), end{a+bgned} where a and b are fixed nonzero real numbers with (a+b neq0) and (ab neq0).
Let r be a given nonzero real number.
Let be a nonzero constant.
Let be a nonzero singular linear map.
