INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK
In this paper, we consider a class of meromorphic functions \(r(z)\) having an \(s\)-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions in the sup-norm on the disk in the complex plane. These results produce so...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2023-07-01
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| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/508 |
| _version_ | 1797769908254146560 |
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| author | Mohd Yousf Mir Shah Lubna Wali Wali Mohammad Shah |
| author_facet | Mohd Yousf Mir Shah Lubna Wali Wali Mohammad Shah |
| author_sort | Mohd Yousf Mir |
| collection | DOAJ |
| description | In this paper, we consider a class of meromorphic functions \(r(z)\) having an \(s\)-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions in the sup-norm on the disk in the complex plane. These results produce some sharper inequalities while taking into account the placement of zeros of the underlying rational function. Moreover, many inequalities for polynomials and polar derivatives follow as special cases. In particular, our results generalize as well as refine a result due Dewan et al. [6]. |
| first_indexed | 2024-03-12T21:15:50Z |
| format | Article |
| id | doaj.art-5c3f0ffd281b42f3b1e8b4c961920a8a |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-03-12T21:15:50Z |
| publishDate | 2023-07-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-5c3f0ffd281b42f3b1e8b4c961920a8a2023-07-29T12:20:16ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522023-07-019110.15826/umj.2023.1.008172INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISKMohd Yousf Mir0Shah Lubna Wali1Wali Mohammad Shah2Department of Mathematics, Central University of Kashmir, Ganderbal-191201Department of Mathematics, Central University of Kashmir, Ganderbal-191201Department of Mathematics, Central University of Kashmir, Ganderbal-191201In this paper, we consider a class of meromorphic functions \(r(z)\) having an \(s\)-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions in the sup-norm on the disk in the complex plane. These results produce some sharper inequalities while taking into account the placement of zeros of the underlying rational function. Moreover, many inequalities for polynomials and polar derivatives follow as special cases. In particular, our results generalize as well as refine a result due Dewan et al. [6].https://umjuran.ru/index.php/umj/article/view/508polynomial, rational function, \(s\)-fold zeros, bernstein inequality. |
| spellingShingle | Mohd Yousf Mir Shah Lubna Wali Wali Mohammad Shah INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK Ural Mathematical Journal polynomial, rational function, \(s\)-fold zeros, bernstein inequality. |
| title | INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK |
| title_full | INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK |
| title_fullStr | INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK |
| title_full_unstemmed | INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK |
| title_short | INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK |
| title_sort | inequalities for a class of meromorphic functions whose zeros are within or outside a given disk |
| topic | polynomial, rational function, \(s\)-fold zeros, bernstein inequality. |
| url | https://umjuran.ru/index.php/umj/article/view/508 |
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