Fixed points of difference operator of meromorphic functions

Let f be a transcendental meromorphic function of order less than one. The authors prove that the exact difference Δf =(z+1)-f(z) has infinitely many fixed points, if a ∈ ℂ and ∞ are Borel exceptional values (or Nevanlinna deficiency values) of f. These results extend the related results obtained by Chen and Shon.