Let f be a transcendental meromorphic function in the complex plane C, and a be a nonzero complex number. We give quantitative estimates for the characteristic function T(r, f) in terms of N(r, 1/(fl (f(k))n –a)), for integers k, l, n greater than 1. We conclude that fl (f(k))n assumes every nonzero finite value infinitely often. © 2016, Hir...