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A proper subclass of Maclane's class ° ’

DOI: 10.1155/s0161171299224635

Keywords: Analytic functions , asymptotic path , tangential approximation , proper subset , construction , unit disc.

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Abstract:

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 f ¢ ° ’ that admits no asymptotic paths of finite length.

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