On zeros and fixed points of differences of meromorphic functions

Let f be a transcendental meromorphic function and g(z) = f (z + 1) − f (z). A number of results are proved concerning the existences of zeros and fixed points of g(z) or g(z)/f (z) which expand results of Bergweiler and Langley [W. Bergweiler, J.K. Langley, Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc. 142 (2007) 133–147]. © 2008 Elsevier Inc. All rights reserved