International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 463-468
doi:10.1155/S0161171299224635
A proper subclass of Maclane's class 𝒜
Lebanese American University, Beirut, Lebanon
Received 26 June 1997; Revised 20 April 1998
Copyright © 1999 May Hamdan. 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.
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.