Entire functions sharing one small function CM with their shifts and difference operators

In this article, we mainly devote to proving uniqueness results for entire functions sharing one small function CM with their shift and difference operator simultaneously. Let f(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f(z), f(z+c), and Δcnf(z) share 0 CM, then f(z + c)≡ Af(z), where A(≠ 0) is a complex constant. Moreover, let a(z), b(z)(≢ 0) ∈ S(f) be periodic entire functions with period f(z)−a(z),f(z+c)−a(z),Δcnf(z)−b(z) share 0 CM, then f(z + c) ≡ f(z).