TY - JOUR AU - Laine, Ilpo AB - ON THE VALUE DISTRIBUTION OF SOME COMPOSITE MEROMORPHIC FUNCTIONS KARI KATAJAMAKI, LIISA KINNUNEN AND ILPO LAINE 1. Introduction The interest in fix-point and factorization theory has led to several papers related to the value distribution of functions of the type fog — Q; see, for example, [3, 5]. W. Bergweiler [4] proved in 1990 that the equation/og = Q has infinitely many solutions in the complex plane, provided / and g are transcendental entire functions and Q is a non-constant polynomial. In [13], we proved that/o g — Q has infinitely many zeros if/is a non-linear entire function of finite order of growth, g is a transcendental entire function of finite lower order and Q is a non-constant entire function such that T(r,Q) = S(r,g). It is natural to extend the study to the meromorphic case. Recently, W. Bergweiler and C.-C. Yang [6] proved the following result. The function fog — Q has infinitely many zeros if/i s meromorphic and transcendental, g is entire and transcendental, fog is of finite order and Q is non-constant rational. In this paper, we show that under certain growth restrictions, the same conclusion remains valid more generally. In fact, we prove the following. TI - On the Value Distribution of Some Composite Meromorphic Functions JF - Bulletin of the London Mathematical Society DO - 10.1112/blms/25.5.445 DA - 1993-09-01 UR - https://www.deepdyve.com/lp/wiley/on-the-value-distribution-of-some-composite-meromorphic-functions-ZF9bUfvbW3 SP - 445 EP - 452 VL - 25 IS - 5 DP - DeepDyve ER -