International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1999 / Article

Open Access

Volume 22 |Article ID 373625 | 6 pages | https://doi.org/10.1155/S0161171299224635

A proper subclass of Maclane's class π’œ

Received26 Jun 1997
Revised20 Apr 1998

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 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 is a proper subclass of 𝒜 by constructing a function f𝒜 that admits no asymptotic paths of finite length.

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.

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