Derivatives of meromorphic functions sharing polynomials with their difference operators - Wang, M.-H.; Chen, J.-F. (Հայաստանի ԳԱԱ)
In this paper, we investigate the uniqueness of meromorphic functions of finite order f(z) concerning their difference operators Δcf(z) and derivatives f′(z) and prove that if Δcf(z) and f′(z) share a(z), b(z), ∞ CM, where a(z) and b(z) are two distinct polynomials, then they assume one of following cases: (1) f′(z) ≡ Δcf(z); (2) f(z) reduces to a polynomial and f′(z)−AΔcf(z) ≡ (1−A)(cnzn+cn−1zn−1+· · ·+c1z+c0), where A(̸= 1) is a nonzero constant and cn, cn−1, · · · , c1, c0 are all constants. This generalizes the corresponding results due to Qi et al. and Deng et al.
Keywords: Mathematics