A proper subclass of Maclane's class 𝒜

May Hamdan

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-6

Abstract:

The MacLane's class 𝒜 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 ℛ of 𝒜 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 ℛ is a proper subclass of 𝒜 by constructing a function f ∈ 𝒜 that admits no asymptotic paths of finite length.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:373625

DOI: 10.1155/S0161171299224635

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