A proper subclass of Maclane's class
The MacLane's class of analytic functions is the class of nonconstant analytic functions in the unit disk that have asymptotic values at a dense subset of the unit circle. In this paper, we define a subclass of consisting of those functions that have asymptotic values at a dense subset of the unit circle reached along rectifiable asymptotic paths. We also show that the class is a proper subclass of by constructing a function that admits no asymptotic paths of finite length.
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