Entire function which shares two distinct finite values IM with two of its difference operators

Abstract

Abstract Suppose that F ≡ 0 is an entire function with hyper-order σ 2 ( F ) < 1 and m , n ( n > m ≥ 1 ) are two integers. If F , Δ η m F and Δ η m F share two values IM, then either F ≡ Δ η m F or Δ η m F ≡ Δ η m F . Moreover, if n = km for some integer k ≥ 2, then Δ η m F ≡ Δ η m F .