Meromorphic Function Sharing Sets with Its Difference Operator or Shifts

Abstract

Let f be a nonconstant meromorphic function, c ∊ ℂ, and let a(z)(≢ 0) ∊ S(f) be a meromorphic function. If f(z) and P(z, f(z)) share the sets {a(z), −a(z)}, {0} CM almost and share {∞} IM almost, where P(z, f(z)) is defined as (1.1), then f(z) ≡ ±P(z, f(z)) or f(z)P(z, f(z)) ≡ ±a2(z). This extends the results due to Chen and Chen (2013), Liu (2009) and Yi (1987).