Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation
Let M f(r) and μ f (r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let l(r) be a continuously differentiable function convex with respect to ln r. We establish that, in order that ln M f(r) ∼ ln μ f (r), r → +∞, for every entire function f such that...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4273 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510403900997632 |
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| author | Filevych, P. V. Филевич, П. В. Филевич, П. В. |
| author_facet | Filevych, P. V. Филевич, П. В. Филевич, П. В. |
| author_sort | Filevych, P. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:45Z |
| description | Let M f(r) and μ f (r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let l(r) be a continuously differentiable function convex with respect to ln r. We establish that, in order that ln M f(r) ∼ ln μ f (r), r → +∞, for every entire function f such that μ f (r) ∼ l(r), r → +∞, it is necessary and sufficient that ln (rl′(r)) = o(l(r)), r → +∞. |
| first_indexed | 2026-03-24T02:56:27Z |
| format | Article |
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| id | umjimathkievua-article-4273 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:56:27Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b7/9da4813a670fd3273b292d710286cdb7.pdf |
| spelling | umjimathkievua-article-42732020-03-18T20:25:45Z Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation Асимптотична поведінка цілих функій з винятковими значениями у співідношенні Бореля Filevych, P. V. Филевич, П. В. Филевич, П. В. Let M f(r) and μ f (r) be, respectively, the maximum of the modulus and the maximum term of an entire function f and let l(r) be a continuously differentiable function convex with respect to ln r. We establish that, in order that ln M f(r) ∼ ln μ f (r), r → +∞, for every entire function f such that μ f (r) ∼ l(r), r → +∞, it is necessary and sufficient that ln (rl′(r)) = o(l(r)), r → +∞. Hexaй $Mf(r)$ i $μf(r)$ — відповідно максимум модуля i максимальний член цілої функції $f$, а $l(r)$ — неперервно диференційовна i опукла відносно $\ln r$ фупкція. Встановлено, що для того щоб $\ln Mf(r) ∼ \ln μf(r), r → +∞$ — для кожпої цілої функції $f$ такої, що $μf(r) ∼ l(r), r → +∞,$ необхідно i досить, щоб $\ln (rl′(r)) = o(l(r)), r → +∞$. Institute of Mathematics, NAS of Ukraine 2001-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4273 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 4 (2001); 522-530 Український математичний журнал; Том 53 № 4 (2001); 522-530 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4273/5250 https://umj.imath.kiev.ua/index.php/umj/article/view/4273/5251 Copyright (c) 2001 Filevych P. V. |
| spellingShingle | Filevych, P. V. Филевич, П. В. Филевич, П. В. Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation |
| title | Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation |
| title_alt | Асимптотична поведінка цілих функій з винятковими значениями у співідношенні Бореля |
| title_full | Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation |
| title_fullStr | Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation |
| title_full_unstemmed | Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation |
| title_short | Asymptotic Behavior of Entire Functions with Exceptional Values in the Borel Relation |
| title_sort | asymptotic behavior of entire functions with exceptional values in the borel relation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4273 |
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