Vol. 67, No. 2, 1976

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On the value distribution of functions meromorphic in the unit disk with a spiral asymptotic value

James Richard Choike

Vol. 67 (1976), No. 2, 339–351

The object in this paper is to examine the value distribution of functions f(z) nonconstant and meromorphic in the unit disk which have an asymptotic value α, finite or infinite, along a spiral boundary path. The main result which we prove is that if Δ(r) is a component of the set of values z such that |f(z) α| < r, r > 0, which contains a boundary path on which f(z) tends to α as |z|→ 1, then f(z) assumes every value in |w α| < r infinitely often in Δ(r) except for at most two values (if Δ(r) is simply-connected, then there is at most one exceptional value).

Mathematical Subject Classification
Primary: 30A70, 30A70
Received: 22 October 1974
Published: 1 December 1976
James Richard Choike