A proper subclass of Maclane's class 𝒜

Hamdan, May

doi:https://doi.org/10.1155/S0161171299224635

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.

Copyright

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

International Journal of Mathematics and Mathematical Sciences

A proper subclass of Maclane's class 𝒜

Abstract

Copyright

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