INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES
Let \(\Re_n\) be the set of all rational functions of the type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial of degree at most \(n\) and \(w(z) = \prod_{j=1}^{n}(z-a_j)\), \(|a_j|>1\) for \(1\leq j\leq n\). In this paper, we set up some results for rational functions with fixed poles and...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
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.
2022-12-01
|
| Series: | Ural Mathematical Journal |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/455 |
| _version_ | 1797971241456369664 |
|---|---|
| author | Nisar Ahmad Rather Mohmmad Shafi Wani Ishfaq Dar |
| author_facet | Nisar Ahmad Rather Mohmmad Shafi Wani Ishfaq Dar |
| author_sort | Nisar Ahmad Rather |
| collection | DOAJ |
| description | Let \(\Re_n\) be the set of all rational functions of the type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial of degree at most \(n\) and \(w(z) = \prod_{j=1}^{n}(z-a_j)\), \(|a_j|>1\) for \(1\leq j\leq n\). In this paper, we set up some results for rational functions with fixed poles and restricted zeros. The obtained results bring forth generalizations and refinements of some known inequalities for rational functions and in turn produce generalizations and refinements of some polynomial inequalities as well. |
| first_indexed | 2024-04-11T03:29:32Z |
| format | Article |
| id | doaj.art-d27822b64460497d871f8fd997caeec5 |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-04-11T03:29:32Z |
| publishDate | 2022-12-01 |
| 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-d27822b64460497d871f8fd997caeec52023-01-02T06:52:22ZengKrasovskii 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 Journal2414-39522022-12-018210.15826/umj.2022.2.012159INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLESNisar Ahmad Rather0Mohmmad Shafi Wani1Ishfaq Dar2University of Kashmir, Hazratbal, Srinagar, Jammu and Kashmir 190006University of Kashmir, Hazratbal, Srinagar, Jammu and Kashmir 190006Institute of Technology, Zakura Campus, University of Kashmir, SrinagarLet \(\Re_n\) be the set of all rational functions of the type \(r(z) = p(z)/w(z),\) where \(p(z)\) is a polynomial of degree at most \(n\) and \(w(z) = \prod_{j=1}^{n}(z-a_j)\), \(|a_j|>1\) for \(1\leq j\leq n\). In this paper, we set up some results for rational functions with fixed poles and restricted zeros. The obtained results bring forth generalizations and refinements of some known inequalities for rational functions and in turn produce generalizations and refinements of some polynomial inequalities as well.https://umjuran.ru/index.php/umj/article/view/455rational functions, polynomials, inequalities |
| spellingShingle | Nisar Ahmad Rather Mohmmad Shafi Wani Ishfaq Dar INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES Ural Mathematical Journal rational functions, polynomials, inequalities |
| title | INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES |
| title_full | INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES |
| title_fullStr | INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES |
| title_full_unstemmed | INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES |
| title_short | INEQUALITIES PERTAINING TO RATIONAL FUNCTIONS WITH PRESCRIBED POLES |
| title_sort | inequalities pertaining to rational functions with prescribed poles |
| topic | rational functions, polynomials, inequalities |
| url | https://umjuran.ru/index.php/umj/article/view/455 |
| work_keys_str_mv | AT nisarahmadrather inequalitiespertainingtorationalfunctionswithprescribedpoles AT mohmmadshafiwani inequalitiespertainingtorationalfunctionswithprescribedpoles AT ishfaqdar inequalitiespertainingtorationalfunctionswithprescribedpoles |