UNIQUENESS RESULTS ON MEROMORPHIC FUNCTIONS AND THEIR DIFFERENCE OPERATORS SHARING TARGETS WITH WEIGHT

Let f be a nonconstant meromorphic function of hyper-order strictly less than 1, and let c ∈ ℂ \ {0} such that f(z + c) ≢ f(z). We prove that if f and its exact difference ∆cf(z) = f(z + c) - f(z) share partially 0, ∞ CM and share 1 IM, then ∆cf = f, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.