UNBOUNDED FATOU COMPONENTS OF COMPOSITE TRANSCENDENTAL MEROMORPHIC FUNCTIONS WITH FINITELY MANY POLES

Abstract

Let $f_i, i=1,2,\ldots,m $ be transcendental meromorphic functions of order less than $\frac{1}{2}$ with at most finitely many poles and at least one of them has positive lower order. Let $g = f_m \circ f_{m-1}\circ \cdots \circ f_1.$ Then either $g$ has no unbounded Fatou components or at least one unbounded Fatou component $g$ is multiply connected.