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 โ 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 โ is a proper subclass of 𝒜 by constructing a function fโ𝒜 that admits no asymptotic paths of finite length.
Citation:
Hamdan, M. (1999). A proper subclass of Maclane's class 𝒜. International Journal of Mathematics and Mathematical Sciences, 22(3), 463-468.
