Picard-Hayman Behavior Of Derivatives Of Meromorphic Functions

Let f be a transcendental meromorphic function on C, and P(z), Q(z) be two polynomials with degP(z) > deg Q(z). In this paper, we prove that: if f (z) double right arrow 0 f'(z) = a(a nonzero constant), except possibly finitely many, then f'(z) - P (z)/Q(z) has infinitely many zeros. Our result extends or improves some previous related results due to Bergweiler-Pang, Pang-Nevo-Zalcman, Wang-Fang, and the author, et. al.