A proper subclass of Maclane's class 𝒜

Hamdan, May

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

International Journal of Mathematics and Mathematical Sciences

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

May Hamdan, "A proper subclass of Maclane's class 𝒜", International Journal of Mathematics and Mathematical Sciences, vol. 22, Article ID 373625, 6 pages, 1999. https://doi.org/10.1155/S0161171299224635

A proper subclass of Maclane's class 𝒜

May Hamdan¹

¹Lebanese American University, Lebanon

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 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.

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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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