%0 Journal Article
%T A proper subclass of Maclane's class  ¡ã   ¡¯
%A May Hamdan
%J International Journal of Mathematics and Mathematical Sciences
%D 1999
%I Hindawi Publishing Corporation
%R 10.1155/s0161171299224635
%X The MacLane's class  ¡ã   ¡¯   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  ¡é     of  ¡ã   ¡¯   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  ¡é     is a proper subclass of  ¡ã   ¡¯   by constructing a function f ¡é     ¡ã   ¡¯   that admits no asymptotic paths of finite length.
%K Analytic functions
%K asymptotic path
%K tangential approximation
%K proper subset
%K construction
%K unit disc.
%U http://dx.doi.org/10.1155/S0161171299224635