A proper subclass of Maclane's class 𝒜
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...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299224635 |
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| _version_ | 1832548447641665536 |
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| author | May Hamdan |
| author_facet | May Hamdan |
| author_sort | May Hamdan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1344578365fc4144ac8fae2ff10498dd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1344578365fc4144ac8fae2ff10498dd2025-02-03T06:14:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122346346810.1155/S0161171299224635A proper subclass of Maclane's class 𝒜May Hamdan0Lebanese American University, Beirut, LebanonThe 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.http://dx.doi.org/10.1155/S0161171299224635Analytic functionsasymptotic pathtangential approximationproper subsetconstructionunit disc. |
| spellingShingle | May Hamdan A proper subclass of Maclane's class 𝒜 International Journal of Mathematics and Mathematical Sciences Analytic functions asymptotic path tangential approximation proper subset construction unit disc. |
| title | A proper subclass of Maclane's class 𝒜 |
| title_full | A proper subclass of Maclane's class 𝒜 |
| title_fullStr | A proper subclass of Maclane's class 𝒜 |
| title_full_unstemmed | A proper subclass of Maclane's class 𝒜 |
| title_short | A proper subclass of Maclane's class 𝒜 |
| title_sort | proper subclass of maclane s class 𝒜 |
| topic | Analytic functions asymptotic path tangential approximation proper subset construction unit disc. |
| url | http://dx.doi.org/10.1155/S0161171299224635 |
| work_keys_str_mv | AT mayhamdan apropersubclassofmaclanesclassa AT mayhamdan propersubclassofmaclanesclassa |