Meromorphic functions sharing one value

Let f and g be two nonconstant meromorphic functions defined in the open complex plane C. If for some a ∈ C∪ {∞}, f − a and g − a have the same set of zeros with the same multiplicities, we say that f and g share the value a CM (counting multiplicities), and if we do not consider the multiplicities, then f and g are said to share the value a IM (ignoring multiplicities). We denote by T(r) the maximum of T(r, f ) and T(r,g). The notation S(r) denotes any quantity satisfying S(r) = o(T(r)) as r → ∞, outside a set of finite linear measure. We use I to denote any set of infinite linear measure of 0 < r <∞. Due to Nevanlinna [9], it is well known that if f and g share four distinct values CM, then f is a Möbius transformation of g. Yang and Hua showed that similar conclusions hold for certain types of differential polynomials when they share only one value. They proved the following result.